Jean-Christophe Jameux
4 years ago
parent
96c33ff6ab
commit
aea1b29f2c
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@ -0,0 +1,25 @@ |
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{ |
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"type": "application", |
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"source-directories": [ |
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"src" |
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], |
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"elm-version": "0.19.1", |
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"dependencies": { |
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"direct": { |
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"elm/browser": "1.0.2", |
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"elm/core": "1.0.5", |
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"elm/html": "1.0.0", |
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"elm/parser": "1.1.0" |
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}, |
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"indirect": { |
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"elm/json": "1.1.3", |
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"elm/time": "1.0.0", |
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"elm/url": "1.0.0", |
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"elm/virtual-dom": "1.0.2" |
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} |
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}, |
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"test-dependencies": { |
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"direct": {}, |
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"indirect": {} |
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} |
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} |
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File diff suppressed because it is too large
Load Diff
@ -0,0 +1,64 @@ |
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module Main exposing (..) |
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|
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-- Press buttons to increment and decrement a counter. |
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-- |
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-- Read how it works: |
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-- https://guide.elm-lang.org/architecture/buttons.html |
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-- |
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|
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|
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import Browser |
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import Html exposing (Html, button, div, text) |
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import Html.Events exposing (onClick) |
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|
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-- MAIN |
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main = |
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Browser.sandbox { init = init, update = update, view = view } |
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|
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-- MODEL |
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type alias Model = Int |
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init : Model |
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init = |
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0 |
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|
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-- UPDATE |
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type Msg |
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= Increment |
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| Decrement |
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update : Msg -> Model -> Model |
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update msg model = |
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case msg of |
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Increment -> |
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model + 1 |
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Decrement -> |
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model - 1 |
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-- VIEW |
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view : Model -> Html Msg |
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view model = |
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div [] |
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[ button [ onClick Decrement ] [ text "-" ] |
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, div [] [ text (String.fromInt model) ] |
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, button [ onClick Increment ] [ text "+" ] |
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] |
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@ -0,0 +1,702 @@ |
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module QCM exposing (..) |
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import Browser |
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import Parser as P exposing (Parser, (|.), (|=), succeed, symbol, float, spaces) |
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import List as L |
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import String as S |
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import Html exposing (Html, Attribute, button, div, input, text, p) |
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import Html.Attributes exposing (..) |
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import Html.Events exposing (onInput, onClick) |
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|
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{- |
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███ ███ █████ ██ ███ ██ |
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████ ████ ██ ██ ██ ████ ██ |
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██ ████ ██ ███████ ██ ██ ██ ██ |
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██ ██ ██ ██ ██ ██ ██ ██ ██ |
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██ ██ ██ ██ ██ ██ ████ |
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-} |
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main = |
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Browser.sandbox { init = init, update = update, view = view } |
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{- |
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███ ███ ██████ ██████ ███████ ██ |
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████ ████ ██ ██ ██ ██ ██ ██ |
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██ ████ ██ ██ ██ ██ ██ █████ ██ |
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-} |
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type alias Model = |
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{ question : String |
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, questions : List String |
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} |
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init : Model |
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init = |
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{ question = "" |
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, questions = [ "" ] |
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} |
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{- |
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██ ██ ██████ ██████ █████ ████████ ███████ |
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██ ██ ██ ██ ██ ██ ██ ██ ██ ██ |
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██ ██ ██████ ██ ██ ███████ ██ █████ |
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██ ██ ██ ██ ██ ██ ██ ██ ██ |
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██████ ██ ██████ ██ ██ ██ ███████ |
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-} |
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type Msg |
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= Question String |
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| GenererQuestion |
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update : Msg -> Model -> Model |
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update msg model = |
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case msg of |
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Question nouvelleQuestion -> |
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{ model | question = nouvelleQuestion } |
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GenererQuestion -> |
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{ model | questions = [ |
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case P.run questions model.question of |
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Ok macro -> voirMacro macro |
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Err _ -> "Y a un truc qui cloche !" |
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] } |
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{- |
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██ ██ ██ ███████ ██ ██ |
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██ ██ ██ ██ ██ ██ |
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██ ██ ██ █████ ██ █ ██ |
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██ ██ ██ ██ ██ ███ ██ |
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████ ██ ███████ ███ ███ |
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-} |
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view : Model -> Html Msg |
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view model = |
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div [] |
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<| input [ placeholder "Format de la question", value model.question, onInput Question ] [] |
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:: button [ onClick GenererQuestion ] [ text "Générer les questions" ] |
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:: ( p [] <| L.map text model.questions ) |
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{- |
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, [ dl05 [0, 4, 2] 5 ] |
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, [ text ( poly [0, 0, 7, -3, 0 , 2, 1 , -1 , 3 , 1, 1, 1, 5] ) ] |
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, [ primitLn01 [-5,-6] ] |
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, [ primitPoly01 [2,-5,1,7] ] -- J'ai oublié de les générer !!!!!!! |
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, [ equaDiff01 -5 ] |
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, [ equaDiff02 [4, -5] ] |
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, [ equaDiff03 [4, -5] ] |
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, [ derivPoly01 [4, -5, 3, 5, 13] ] |
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, [ derivPoly02 [-3, -4, 2, 7, -13] ] |
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, [ dl01 [-5, -2, 2, -1] ] |
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, [ dl02 [-5, 0, -2, -1] ] |
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, [ dl03 [0, -8, 0, 7] ] |
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, [ dl04 [-1, 2, 0, -3] ] |
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, List.map equaDiff01 <| List.range -99 -2 -- 98 possibilités OK |
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, List.map equaDiff02 ( mix [ [3,5,9,11,13,17,27,15,25,27], [-2,-4,-7,-8,-14,-16,-19,-23,-28,-29] ] ) -- 100 possibilités OK |
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, List.map equaDiff03 ( mix [ [3,5,9,11,13,17,27,15,25,27], [-2,-4,-7,-8,-14,-16,-19,-23,-28,-29] ] ) -- 100 possibilités OK |
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-- Pourries par un List.range -2 1 ++ List.range 1 2 qui passe à 900 et 768 possibilités dans evalbox, dont répétitions |
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, List.map derivPoly01 ( mix [ [2,4,6], List.range -6 -2, List.range 2 6, List.range -2 -1 ++ List.range 1 2, List.range 11 12 ] ) -- 600 possibilités |
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, List.map derivPoly02 ( mix [ [-9,-7,-5,-3], [-8,-6,-4,-2], [2,4,6,8], List.range -2 -1 ++ List.range 1 2, List.range -12 -11 ] ) -- 512 possibilités |
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, List.map primitLn01 ( mix [ List.range -9 -2 ++ List.range 2 9, List.range -9 -2 ++ List.range 2 9 ] ) -- 256 possibilités OK |
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, List.map dl01 ( mix [ [-5,-3,-1,1,3,5], [-6,-4,-2,2,4,6], [1,2,3], [-3,-2,-1,1,2,3] ] ) -- 648 possibilités OK |
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, List.map dl02 ( mix [ [-5,-4,-3,-2,-1,1,2,3,4,5], [0], [-1,-2,-3,-4,-5], [-3,-2,-1,1,2,3] ] ) -- 300 possibilités (toutes les questions en double because import pourri) |
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, List.map dl03 ( mix [ [0], [-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9], [0], [1,2,3,4,5,6,7,8,9] ] ) -- 162 possibilités OK |
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, List.map dl04 ( mix [ [-5,-3,-1,1,3,5], [-6,-4,-2,2,4,6], [0], [-9,-8,-7,-6,-5,-4,-3,-2,-1] ] ) --324 possibilités Ok |
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, List.concat <| List.map ( mapTwist [3,5,9] ) ( List.map dl05 ( mix [ [0], [2,4,7,8,11,13,16,17], [2,4,7,8,11,13,16,17] ] ) ) -- 192 possibilités OK |
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, d3 -- 512 possibilités OK |
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-} |
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:: ( List.map primitPoly01 <| mix [ List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3 ] ) -- 256 possibilités OK |
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{- |
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██████ █████ ██████ ███████ ███████ ██████ |
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██ ██ ██ ██ ██ ██ ██ ██ ██ ██ |
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██████ ███████ ██████ ███████ █████ ██████ |
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██ ██ ██ ██ ██ ██ ██ ██ ██ |
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██ ██ ██ ██ ██ ███████ ███████ ██ ██ |
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-} |
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type TexteVariable |
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= Texte String |
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| Variable String |
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type alias Macro |
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= List TexteVariable |
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voirMacro macro |
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= S.concat <| L.map voirTexteVariable macro |
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voirTexteVariable txtvar |
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= case txtvar of |
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Texte txt -> txt |
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Variable var -> var |
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questionOld : Parser Macro |
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questionOld = |
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succeed (\x -> x :: []) |
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|= P.oneOf [ expressionVariable , texteSansVariables ] |
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{-- |
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|= succeed Texte |
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|= ( |
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P.getChompedString |
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<| succeed () |
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|. P.chompUntilEndOr "\n" |
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) |
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--} |
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texteSansVariables : Parser TexteVariable |
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texteSansVariables |
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= succeed Texte |
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|= P.getChompedString ( |
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succeed () |
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|. P.chompIf ( (/=) '#' ) |
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|. P.chompWhile ( (/=) '#' ) |
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) |
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expressionVariable : Parser TexteVariable |
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expressionVariable |
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= succeed Variable |
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|. symbol "#(" |
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|= (P.getChompedString <| |
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succeed () |
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|. P.chompUntil "#") |
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{-- |
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testDeChomp |
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= succeed ( (::) ) |
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( |
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P.getChompedString |
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<| succeed () |
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|. P.chompUntil "truc" |
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) |
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|= P.int |
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--} |
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parserBis : Parser Macro |
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parserBis |
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= succeed (\x y-> Texte x :: y :: []) |
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|= P.getChompedString ( P.chompWhile ( (/=) '#' ) ) |
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|= P.oneOf [ expressionVariable , texteSansVariables ] |
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--|= question |
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questions : Parser Macro |
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questions = |
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P.loop [] questionsBis |
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questionsBis : Macro -> Parser (P.Step Macro Macro) |
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questionsBis ls = |
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P.oneOf |
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[ succeed (\l -> P.Loop (l :: ls)) |
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|= P.oneOf [ expressionVariable , texteSansVariables ] |
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, succeed () |
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|> P.map (\_ -> P.Done (List.reverse ls)) |
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] |
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type Expr num |
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= Const num |
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| Var String |
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| Poly ( List num ) |
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| Exp ( Expr num ) |
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| Ln ( Expr num ) |
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| Sin ( Expr num ) |
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| Cos ( Expr num ) |
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| Prod ( Expr num ) ( Expr num ) |
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| Quot ( Expr num ) ( Expr num ) |
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| Sum ( Expr num ) ( Expr num ) |
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| Diff ( Expr num ) ( Expr num ) |
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| Power ( Expr num ) num |
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mathTeX a = "$" ++ a ++ "$" |
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fonction a = "x\\mapsto " ++ a |
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affineExp a b c |
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= if (a,b) == (0,0) then "0" |
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else if (a,c) == (0,1) then String.fromInt b ++ "e^x" |
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else if a == 0 then String.fromInt b ++ "e^{" ++ (String.fromInt c) ++ "x}" |
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else if (a,b,c) == (1,0,1) then "xe^x" |
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else if (b,c) == (0,1) then (String.fromInt a) ++ "x" ++ "e^x" |
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else if b == 0 then (String.fromInt a) ++ "x" ++ "e^{" ++ (String.fromInt c) ++ "x}" |
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else if c == 1 then "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^x" |
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else "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}" |
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derivExp01 a b c = |
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let |
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f aa bb cc = mathTeX ( fonction ( affineExp aa bb cc ) ) |
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vr aa bb cc = p [] [ text ( "+" ++ ( f aa bb cc) ) ] |
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fx aa bb cc = p [] [ text ( "-" ++ ( f aa bb cc) ) ] |
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in |
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div [] |
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[ p [] [ text ("Donner la dérivée de la fonction " ++ f a b c) ] |
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, vr (a*c) (a+b*c) c |
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, fx (a+b) a c |
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, fx (a+b) a c |
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, fx (a+b*c) (a*c) c |
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, fx (a-b*c) (a*c) c |
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, fx (a-b*c) (a*c) c |
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, fx a 0 c |
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, fx (a*c) 0 c |
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, fx a 0 1 |
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, fx (a*c) 0 1 |
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{-- |
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, p [] [ text ("----") ] |
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, p [] [ text ("Avant toute chose, il faut bien voir que $\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}$ est de la forme $uv$ avec $u=ax+b$ et $v=e^{cx}$.") ], |
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, p [] [ text ("Ensuite, il faut savoir que la dérivée de $uv$ est donnée par $u'v+uv'$, et que la dérivée de $e^{u}$ est donnée par $e^{u}\\cdot u'$, ce qui dans notre cas nous donne que la dérivée de $e^{" ++ (String.fromInt c) ++ "x}$ est donnée par $" ++ (String.fromInt c) ++ "e^{" ++ (String.fromInt c) ++ "x}$.") ] |
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, p [] [ text ("Nous avons donc que la dérivée de la fonction est :") ] |
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, p [] [ text ("$\\begin{array}{rl} x\\mapsto & " ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt c) ++ "x}+\\left(" ++ (String.fromInt (a)) ++ "x+" ++ (String.fromInt (b)) ++ "\\right)ce^{" ++ (String.fromInt (c)) ++ "x}\\\\& =" ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt (c)) ++ "x}+\\left(" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a)) ++ "+" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a+b*c)) ++ "+" ++ (String.fromInt (a*c)) ++ "x\\right)e^{" ++ (String.fromInt (c)) ++ "x} \\end{array}$") ] |
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--} |
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, p [] [ text ("==== Dérivées, Exponentielle, derivExp01") ] |
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] |
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|
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-- Des DL |
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monome a n = |
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if a == 0 then "" |
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else if n == 0 then ( String.fromInt a ) |
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else if (n,a) == (1,1) then "x" |
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else if (n,a) == (1,-1) then "-x" |
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else if n == 1 then ( String.fromInt a ) ++ "x" |
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else if a == 1 then "x^{" ++ ( String.fromInt n ) ++ "}" |
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else if a == -1 then "-x^{" ++ ( String.fromInt n ) ++ "}" |
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else ( String.fromInt a ) ++ "x^{" ++ ( String.fromInt n ) ++ "}" |
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poly a_ks = |
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if a_ks == [] then "0" |
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else polyBis a_ks ( List.length a_ks - 1 ) |
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polyBis a_ks n = |
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case a_ks of |
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[] -> "" |
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a_n :: a_kss -> |
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if a_n == 0 then polyBis a_kss ( n - 1 ) |
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else ( monome a_n n ) ++ ( polyGen a_kss ( n - 1 ) ) |
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polyGen a_ks n = |
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case a_ks of |
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[] -> "" |
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a_i :: a_is -> |
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if a_i <= 0 then ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) ) |
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else "+" ++ ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) ) |
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dl a_ks = |
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if a_ks == [] then "0" |
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else dlBis a_ks 0 |
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dlBis a_ks n = |
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case a_ks of |
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[] -> "" |
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premierCoef :: suite -> |
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if premierCoef == 0 then dlBis suite ( n + 1 ) |
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else ( monome premierCoef n ) ++ ( dlGen suite ( n + 1 ) ) |
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|
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dlGen a_ks n = |
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case a_ks of |
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[] -> "" |
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a_i :: a_is -> |
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if a_i <= 0 then ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) ) |
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else "+" ++ ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) ) |
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dl01 a_k = |
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let |
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vr texte = p [] [ text ( "+" ++ texte ) ] |
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fx texte = p [] [ text ( "-" ++ texte ) ] |
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in |
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div [] |
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[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
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, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
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, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
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, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
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, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1 |
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, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
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, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
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, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
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, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
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, vr "$C$ est au-dessus de $T_0$." |
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, fx "$C$ est au-dessous de $T_0$." |
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, fx "$C$ est au-dessous puis au-dessus de $T_0$." |
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, fx "$C$ est au-dessus puis au-dessous de $T_0$." |
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{-- |
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, p [] [ text ("----") ] |
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--} |
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, p [] [ text ("==== Développements limités, Tangentes, dl01") ] |
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] |
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|
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dl02 a_k = |
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let |
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vr texte = p [] [ text ( "+" ++ texte ) ] |
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fx texte = p [] [ text ( "-" ++ texte ) ] |
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in |
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div [] |
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[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 3 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 3 a_k ) ++"x$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx "$C$ est au-dessus de $T_0$." |
||||
, vr "$C$ est au-dessous de $T_0$." |
||||
, fx "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl02") ] |
||||
] |
||||
|
||||
|
||||
dl03 a_k = |
||||
let |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1 |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx "$C$ est au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessous de $T_0$." |
||||
, vr "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl03") ] |
||||
] |
||||
|
||||
|
||||
dl04 a_k = |
||||
let |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1 |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx "$C$ est au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessous de $T_0$." |
||||
, fx "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, vr "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl04") ] |
||||
] |
||||
|
||||
|
||||
dl05 a_k k = -- À n'utiliser qu'avec a_0 = 0 !!! |
||||
let |
||||
coefLin = |
||||
case a_k of |
||||
[] -> 0 |
||||
a_0 :: [] -> 0 |
||||
a_0 :: a_1 :: a_ks -> a_1 |
||||
coefQuad = |
||||
case a_k of |
||||
[] -> 0 |
||||
a_0 :: [] -> 0 |
||||
a_0 :: a_1 :: [] -> 0 |
||||
a_0 :: a_1 :: a_2 :: a_ks -> a_2 |
||||
vr a b = p [] [ text <| "+$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ] |
||||
ffx a b = p [] [ text <| "-$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ] |
||||
fx a = p [] [ text <| "-$" ++ String.fromInt a ++ "$" ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 2 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text <| "Que vaut $\\lim\\limits_{x\\to0}\\frac{f\\left(x\\right)}{" ++ (String.fromInt k) ++ "x}$" ] |
||||
, vr coefLin k |
||||
, ffx 1 coefLin |
||||
, ffx 1 coefQuad |
||||
, ffx 1 k |
||||
, ffx coefQuad k |
||||
, ffx k coefQuad |
||||
, fx coefLin |
||||
, fx coefQuad |
||||
, fx k |
||||
, fx 1 |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl05") ] |
||||
] |
||||
|
||||
|
||||
mapTwist a b = List.map b a |
||||
|
||||
entiers = List.range 2 9 |
||||
|
||||
d1 = List.map derivExp01 entiers |
||||
|
||||
d2 = List.concat ( List.map (mapTwist entiers) d1 ) |
||||
|
||||
d3 = List.concat ( List.map (mapTwist entiers) d2 ) |
||||
|
||||
mix lls = |
||||
case lls of |
||||
[] -> [] |
||||
[] :: llss -> [] |
||||
l :: [] -> List.map List.singleton l |
||||
(a :: ls) :: llss -> ( List.map ( (::) a ) ( mix llss ) ) ++ mix ( ls :: llss ) |
||||
|
||||
derivPoly01 param = -- on donne a pair et positif, les deux racines x_1 < x_2, d, et m > x_2 |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: [] -> div [] [] |
||||
a :: b :: c :: [] -> div [] [] |
||||
a :: b :: c :: d :: [] -> div [] [] |
||||
a :: b :: c :: d :: e :: a_ks -> derivPoly01Bis a b c d e |
||||
|
||||
derivPoly01Bis a x_1 x_2 d m = |
||||
let |
||||
b = 0 - 3*a*(x_1 + x_2)//2 |
||||
c = 3*a*x_1*x_2 |
||||
a_k = [a,b,c,d] |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$." |
||||
, fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$." |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$" |
||||
, vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$" |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Dérivée, Polynômes, derivPoly01") ] |
||||
] |
||||
|
||||
derivPoly02 param = -- on donne a impair et négatif, les deux racines x_1 < x_2 pairs distincs, d, et m < x_1 |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: [] -> div [] [] |
||||
a :: b :: c :: [] -> div [] [] |
||||
a :: b :: c :: d :: [] -> div [] [] |
||||
a :: b :: c :: d :: e :: a_ks -> derivPoly02Bis a b c d e |
||||
|
||||
derivPoly02Bis a x_1 x_2 d m = |
||||
let |
||||
b = 0 - 3*a*(x_1 + x_2)//2 |
||||
c = 3*a*x_1*x_2 |
||||
a_k = [a,b,c,d] |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$." |
||||
, fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$." |
||||
, vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right]$" |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right[$" |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Dérivée, Polynômes, derivPoly02") ] |
||||
] |
||||
|
||||
polyD a_ks = polyDbis a_ks ( List.length a_ks - 1 ) |
||||
|
||||
polyDbis a_ks n = |
||||
case a_ks of |
||||
[] -> [] |
||||
a_0 :: [] -> [] |
||||
a_k :: a_kss -> ( n*a_k ) :: polyDbis a_kss ( n - 1 ) |
||||
|
||||
equaDiff01 a = -- a négatif |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y$ ?" ] |
||||
, vr <| String.fromInt ( a - 1 ) ++ "e^{" ++ String.fromInt a ++ "x}" |
||||
, vr <| String.fromInt ( a + 4 ) ++ "e^{" ++ String.fromInt a ++ "x}" |
||||
, vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt (a-1) ++ "x}" |
||||
, fx <| String.fromInt ( a - 3 ) ++ "e^x" |
||||
, fx <| String.fromInt ( a + 7 ) ++ "e^x" ++ String.fromInt a |
||||
, fx <| String.fromInt a ++ "e^x" |
||||
, fx <| String.fromInt a ++ "e^x+" ++ String.fromInt ( a + 100) |
||||
, fx <| String.fromInt ( a - 1 ) ++ "e^x+" ++ String.fromInt ( a + 100) |
||||
, fx <| String.fromInt ( a - 8 ) ++ "e^{" ++ String.fromInt (a-1) ++ "x}" ++ String.fromInt a |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Équations différentielles, equaDiff01") ] |
||||
] |
||||
|
||||
equaDiff02 param = |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: c -> equaDiff02Bis a b |
||||
|
||||
equaDiff02Bis a b = -- a positif, b négatif, pas de simplification |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $" ++ String.fromInt a ++"y'=" ++ String.fromInt b ++ "y$ ?" ] |
||||
, vr <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, vr <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Équations différentielles, equaDiff02") ] |
||||
] |
||||
|
||||
equaDiff03 param = |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: c -> equaDiff03Bis a b |
||||
|
||||
equaDiff03Bis a b = -- a positif, b négatif, pas de simplification |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y" ++ String.fromInt b ++"$ ?" ] |
||||
, fx <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, vr <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Équations différentielles, equaDiff03") ] |
||||
] |
||||
|
||||
primitLn01 a_k = |
||||
case a_k of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: c -> primitLn01Bis a b |
||||
|
||||
primitLn01Bis a b = |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
axpb = poly [a,b] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f <| "\\frac{" ++ String.fromInt a ++ "}{" ++ axpb ++ "}" ) ++ " ?" ] |
||||
, vr <| "\\ln\\left(" ++ axpb ++ "\\right)" |
||||
, vr <| "\\ln\\left(" ++ axpb ++ "\\right)+" ++ String.fromInt ( b + 30 ) |
||||
, vr <| "\\ln\\left(" ++ axpb ++ "\\right)" ++ String.fromInt ( a - 20) |
||||
, fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
, fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 ) |
||||
, fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
, fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}+" ++ String.fromInt ( b + 30 ) |
||||
, fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( a - 20) |
||||
, fx <| "\\frac{" ++ poly [a*a, a*b+a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
, fx <| "\\frac{" ++ poly [a*a, a*b-a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Primitives, Logarithme, primitLn01") ] |
||||
] |
||||
|
||||
primitPoly01 a_k = |
||||
case a_k of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: [] -> div [] [] |
||||
a :: b :: c :: [] -> div [] [] |
||||
a :: b :: c :: d :: e -> primitPoly01Bis a b c d |
||||
|
||||
primitPoly01Bis a b c d = |
||||
let |
||||
pol = [a,b,c,d,0] |
||||
polD = polyD pol |
||||
polDD = polyD polD |
||||
f a_k = mathTeX ( fonction ( poly a_k ) ) |
||||
vr a_k = p [] [ text ( "+" ++ ( f a_k ) ) ] |
||||
fx a_k = p [] [ text ( "-" ++ ( f a_k ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f polD ) ++ " ?" ] |
||||
, vr <| List.map2 (+) pol [0,0,0,0,5] |
||||
, vr <| List.map2 (+) pol [0,0,0,0,-8] |
||||
, vr <| List.map2 (+) pol [0,0,0,0,8] |
||||
, fx <| List.map2 (+) polD [0,0,0,8] |
||||
, fx <| List.map2 (+) polD [0,0,0,-5] |
||||
, fx <| List.map2 (+) polD [0,0,0,-8] |
||||
, fx <| List.map2 (+) polDD [0,0,8] |
||||
, fx <| List.map2 (+) polDD [0,0,-5] |
||||
, fx <| List.map2 (+) polDD [0,0,-8] |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Primitives, Polynômes, primitPoly01") ] |
||||
] |
||||
|
||||
|
||||
|
||||
|
||||
@ -0,0 +1,583 @@ |
||||
module QCMbis exposing (..) |
||||
|
||||
-- Press buttons to increment and decrement a counter. |
||||
-- |
||||
-- Read how it works: |
||||
-- https://guide.elm-lang.org/architecture/buttons.html |
||||
-- |
||||
|
||||
|
||||
import Browser |
||||
import Html exposing (Html, button, div, text, p) |
||||
import Html.Events exposing (onClick) |
||||
|
||||
|
||||
|
||||
-- MAIN |
||||
|
||||
|
||||
main = |
||||
Browser.sandbox { init = init, update = update, view = view } |
||||
|
||||
|
||||
|
||||
-- MODEL |
||||
|
||||
|
||||
type alias Model = Int |
||||
|
||||
|
||||
init : Model |
||||
init = |
||||
0 |
||||
|
||||
|
||||
|
||||
-- UPDATE |
||||
|
||||
|
||||
type Msg |
||||
= Increment |
||||
| Decrement |
||||
|
||||
|
||||
update : Msg -> Model -> Model |
||||
update msg model = |
||||
case msg of |
||||
Increment -> |
||||
model + 1 |
||||
|
||||
Decrement -> |
||||
model - 1 |
||||
|
||||
|
||||
|
||||
-- VIEW |
||||
|
||||
|
||||
view : Model -> Html Msg |
||||
view model = |
||||
div [] ( List.concat |
||||
[ |
||||
{-- |
||||
, [ dl10 [0, 4, 2] 5 ] |
||||
, [ text ( poly [0, 0, 7, -3, 0 , 2, 1 , -1 , 3 , 1, 1, 1, 5] ) ] |
||||
, [ primitPoly02 [2,-5,1,7] ] |
||||
, [ primitLn02 [-5,-6] ] |
||||
, [ equaDiff04 -5 ] |
||||
, [ equaDiff05 [4, -5] ] |
||||
, [ equaDiff06 [4, -5] ] |
||||
, [ derivPoly03 [4, -5, 3, 5, 13] ] |
||||
, [ derivPoly04 [-3, -4, 2, 7, -13] ] |
||||
, [ dl06 [-5, -2, 2, -1] ] |
||||
, [ dl07 [-5, 0, -2, -1] ] |
||||
, [ dl08 [0, -8, 0, 7] ] |
||||
, [ dl09 [-1, 2, 0, -3] ] |
||||
--} |
||||
List.map equaDiff04 <| List.range -9 -2 -- 98 possibilités |
||||
, List.map equaDiff05 ( mix [ [3,5,7], [-2,-4,-7,-8] ] ) -- 99 possibilités |
||||
, List.map equaDiff06 ( mix [ [3,5,7], [-2,-4,-7,-8] ] ) -- 99 possibilités |
||||
, List.map derivPoly03 ( mix [ [4,6], List.range -7 -6, List.range 2 3, List.range 11 12 ] ) -- 576 possibilités |
||||
, List.map derivPoly04 ( mix [ [-5,-3], [-4,-2], [2,6], List.range -14 -13 ] ) -- 256 possibilités |
||||
, List.map primitLn02 ( mix [ List.range -3 -2 ++ List.range 2 3, List.range -5 -4 ++ List.range 5 6 ] ) -- 256 possibilités |
||||
, List.map primitPoly02 ( mix [ List.range -3 -2 , List.range 2 3, List.range -5 -4 , List.range 6 7 ] ) -- 256 possibilités |
||||
, List.map dl06 ( mix [ [-3,5], [-2,6], [2,3], [-2,3] ] ) -- 648 possibilités |
||||
, List.map dl07 ( mix [ [-5,-2,2], [0], [-3,-4], [-2,3] ] ) -- 300 possibilités |
||||
, List.map dl08 ( mix [ [0], [-3,-2,2,3], [0], [2,3,4,5] ] ) -- 162 possibilités |
||||
, List.map dl09 ( mix [ [-5,3,5], [-6,4], [0], [-5,-3] ] ) --324 possibilités |
||||
, List.concat <| List.map ( mapTwist [3,5,9] ) ( List.map dl10 ( mix [ [0], [2,4], [7,8] ] ) ) -- 192 possibilités |
||||
, d3 -- 729 possibilités |
||||
] |
||||
) |
||||
|
||||
{-- |
||||
type Fonction num |
||||
= Const num |
||||
| X |
||||
| Poly List num |
||||
| Exp Fonction |
||||
| Ln Fonction |
||||
| Sin Fonction |
||||
| Cos Fonction |
||||
--} |
||||
|
||||
|
||||
mathTeX a = "$" ++ a ++ "$" |
||||
|
||||
fonction a = "x\\mapsto " ++ a |
||||
|
||||
affineExp a b c |
||||
= if (a,b) == (0,0) then "0" |
||||
else if (a,c) == (0,1) then String.fromInt b ++ "e^x" |
||||
else if a == 0 then String.fromInt b ++ "e^{" ++ (String.fromInt c) ++ "x}" |
||||
else if (a,b,c) == (1,0,1) then "xe^x" |
||||
else if (b,c) == (0,1) then (String.fromInt a) ++ "x" ++ "e^x" |
||||
else if b == 0 then (String.fromInt a) ++ "x" ++ "e^{" ++ (String.fromInt c) ++ "x}" |
||||
else if c == 1 then "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^x" |
||||
else "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}" |
||||
|
||||
derivExp02 a b c = |
||||
let |
||||
f aa bb cc = mathTeX ( fonction ( affineExp aa bb cc ) ) |
||||
vr aa bb cc = p [] [ text ( "+" ++ ( f aa bb cc) ) ] |
||||
fx aa bb cc = p [] [ text ( "-" ++ ( f aa bb cc) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ("Donner la dérivée de la fonction " ++ f a b c) ] |
||||
, vr (a*c) (a+b*c) c |
||||
, fx (a+b) a c |
||||
, fx (a+b) a c |
||||
, fx (a+b*c) (a*c) c |
||||
, fx (a-b*c) (a*c) c |
||||
, fx (a-b*c) (a*c) c |
||||
, fx a 0 c |
||||
, fx (a*c) 0 c |
||||
, fx a 0 1 |
||||
, fx (a*c) 0 1 |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
, p [] [ text ("Avant toute chose, il faut bien voir que $\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}$ est de la forme $uv$ avec $u=ax+b$ et $v=e^{cx}$.") ], |
||||
, p [] [ text ("Ensuite, il faut savoir que la dérivée de $uv$ est donnée par $u'v+uv'$, et que la dérivée de $e^{u}$ est donnée par $e^{u}\\cdot u'$, ce qui dans notre cas nous donne que la dérivée de $e^{" ++ (String.fromInt c) ++ "x}$ est donnée par $" ++ (String.fromInt c) ++ "e^{" ++ (String.fromInt c) ++ "x}$.") ] |
||||
, p [] [ text ("Nous avons donc que la dérivée de la fonction est :") ] |
||||
, p [] [ text ("$\\begin{array}{rl} x\\mapsto & " ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt c) ++ "x}+\\left(" ++ (String.fromInt (a)) ++ "x+" ++ (String.fromInt (b)) ++ "\\right)ce^{" ++ (String.fromInt (c)) ++ "x}\\\\& =" ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt (c)) ++ "x}+\\left(" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a)) ++ "+" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a+b*c)) ++ "+" ++ (String.fromInt (a*c)) ++ "x\\right)e^{" ++ (String.fromInt (c)) ++ "x} \\end{array}$") ] |
||||
--} |
||||
, p [] [ text ("==== Dérivées, Exponentielle, derivExp02") ] |
||||
] |
||||
|
||||
|
||||
|
||||
-- Des DL |
||||
|
||||
monome a n = |
||||
if a == 0 then "" |
||||
else if n == 0 then ( String.fromInt a ) |
||||
else if (n,a) == (1,1) then "x" |
||||
else if (n,a) == (1,-1) then "-x" |
||||
else if n == 1 then ( String.fromInt a ) ++ "x" |
||||
else if a == 1 then "x^{" ++ ( String.fromInt n ) ++ "}" |
||||
else if a == -1 then "-x^{" ++ ( String.fromInt n ) ++ "}" |
||||
else ( String.fromInt a ) ++ "x^{" ++ ( String.fromInt n ) ++ "}" |
||||
|
||||
poly a_ks = |
||||
if a_ks == [] then "0" |
||||
else polyBis a_ks ( List.length a_ks - 1 ) |
||||
|
||||
polyBis a_ks n = |
||||
case a_ks of |
||||
[] -> "" |
||||
a_n :: a_kss -> |
||||
if a_n == 0 then polyBis a_kss ( n - 1 ) |
||||
else ( monome a_n n ) ++ ( polyGen a_kss ( n - 1 ) ) |
||||
|
||||
polyGen a_ks n = |
||||
case a_ks of |
||||
[] -> "" |
||||
a_i :: a_is -> |
||||
if a_i <= 0 then ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) ) |
||||
else "+" ++ ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) ) |
||||
|
||||
dl a_ks = |
||||
if a_ks == [] then "0" |
||||
else dlBis a_ks 0 |
||||
|
||||
dlBis a_ks n = |
||||
case a_ks of |
||||
[] -> "" |
||||
premierCoef :: suite -> |
||||
if premierCoef == 0 then dlBis suite ( n + 1 ) |
||||
else ( monome premierCoef n ) ++ ( dlGen suite ( n + 1 ) ) |
||||
|
||||
dlGen a_ks n = |
||||
case a_ks of |
||||
[] -> "" |
||||
a_i :: a_is -> |
||||
if a_i <= 0 then ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) ) |
||||
else "+" ++ ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) ) |
||||
|
||||
dl06 a_k = |
||||
let |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1 |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, vr "$C$ est au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessous de $T_0$." |
||||
, fx "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl06") ] |
||||
] |
||||
|
||||
|
||||
dl07 a_k = |
||||
let |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 3 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 3 a_k ) ++"x$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx "$C$ est au-dessus de $T_0$." |
||||
, vr "$C$ est au-dessous de $T_0$." |
||||
, fx "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl07") ] |
||||
] |
||||
|
||||
|
||||
dl08 a_k = |
||||
let |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1 |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx "$C$ est au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessous de $T_0$." |
||||
, vr "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl08") ] |
||||
] |
||||
|
||||
|
||||
dl09 a_k = |
||||
let |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1 |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$" |
||||
, fx "$C$ est au-dessus de $T_0$." |
||||
, fx "$C$ est au-dessous de $T_0$." |
||||
, fx "$C$ est au-dessous puis au-dessus de $T_0$." |
||||
, vr "$C$ est au-dessus puis au-dessous de $T_0$." |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl09") ] |
||||
] |
||||
|
||||
|
||||
dl10 a_k k = -- À n'utiliser qu'avec a_0 = 0 !!! |
||||
let |
||||
coefLin = |
||||
case a_k of |
||||
[] -> 0 |
||||
a_0 :: [] -> 0 |
||||
a_0 :: a_1 :: a_ks -> a_1 |
||||
coefQuad = |
||||
case a_k of |
||||
[] -> 0 |
||||
a_0 :: [] -> 0 |
||||
a_0 :: a_1 :: [] -> 0 |
||||
a_0 :: a_1 :: a_2 :: a_ks -> a_2 |
||||
vr a b = p [] [ text <| "+$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ] |
||||
ffx a b = p [] [ text <| "-$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ] |
||||
fx a = p [] [ text <| "-$" ++ String.fromInt a ++ "$" ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 2 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ] |
||||
, p [] [ text <| "Que vaut $\\lim\\limits_{x\\to0}\\frac{f\\left(x\\right)}{" ++ (String.fromInt k) ++ "x}$" ] |
||||
, vr coefLin k |
||||
, ffx 1 coefLin |
||||
, ffx 1 coefQuad |
||||
, ffx 1 k |
||||
, ffx coefQuad k |
||||
, ffx k coefQuad |
||||
, fx coefLin |
||||
, fx coefQuad |
||||
, fx k |
||||
, fx 1 |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Développements limités, Tangentes, dl10") ] |
||||
] |
||||
|
||||
|
||||
mapTwist a b = List.map b a |
||||
|
||||
entiers = List.range 2 4 |
||||
|
||||
d1 = List.map derivExp02 entiers |
||||
|
||||
d2 = List.concat ( List.map (mapTwist entiers) d1 ) |
||||
|
||||
d3 = List.concat ( List.map (mapTwist entiers) d2 ) |
||||
|
||||
mix lls = |
||||
case lls of |
||||
[] -> [] |
||||
[] :: llss -> [] |
||||
l :: [] -> List.map List.singleton l |
||||
(a :: ls) :: llss -> ( List.map ( (::) a ) ( mix llss ) ) ++ mix ( ls :: llss ) |
||||
|
||||
derivPoly03 param = -- on donne a pair et positif, les deux racines x_1 < x_2, d, et m > x_2 |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: [] -> div [] [] |
||||
a :: b :: c :: [] -> div [] [] |
||||
a :: b :: c :: d :: [] -> div [] [] |
||||
a :: b :: c :: d :: e :: a_ks -> derivPoly03Bis a b c d e |
||||
|
||||
derivPoly03Bis a x_1 x_2 d m = |
||||
let |
||||
b = 0 - 3*a*(x_1 + x_2)//2 |
||||
c = 3*a*x_1*x_2 |
||||
a_k = [a,b,c,d] |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$." |
||||
, fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$." |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$" |
||||
, vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$" |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Dérivée, Polynômes, derivPoly03") ] |
||||
] |
||||
|
||||
derivPoly04 param = -- on donne a impair et négatif, les deux racines x_1 < x_2 pairs distincs, d, et m < x_1 |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: [] -> div [] [] |
||||
a :: b :: c :: [] -> div [] [] |
||||
a :: b :: c :: d :: [] -> div [] [] |
||||
a :: b :: c :: d :: e :: a_ks -> derivPoly04Bis a b c d e |
||||
|
||||
derivPoly04Bis a x_1 x_2 d m = |
||||
let |
||||
b = 0 - 3*a*(x_1 + x_2)//2 |
||||
c = 3*a*x_1*x_2 |
||||
a_k = [a,b,c,d] |
||||
vr texte = p [] [ text ( "+" ++ texte ) ] |
||||
fx texte = p [] [ text ( "-" ++ texte ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ] |
||||
, p [] [ text ( "Cocher la ou les réponses correctes." ) ] |
||||
, vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$." |
||||
, fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$." |
||||
, vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$" |
||||
, vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right]$" |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right[$" |
||||
, fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
, fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Dérivée, Polynômes, derivPoly04") ] |
||||
] |
||||
|
||||
polyD a_ks = polyDbis a_ks ( List.length a_ks - 1 ) |
||||
|
||||
polyDbis a_ks n = |
||||
case a_ks of |
||||
[] -> [] |
||||
a_0 :: [] -> [] |
||||
a_k :: a_kss -> ( n*a_k ) :: polyDbis a_kss ( n - 1 ) |
||||
|
||||
equaDiff04 a = -- a négatif |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y$ ?" ] |
||||
, vr <| String.fromInt ( a - 1 ) ++ "e^{" ++ String.fromInt a ++ "x}" |
||||
, vr <| String.fromInt ( a + 4 ) ++ "e^{" ++ String.fromInt a ++ "x}" |
||||
, vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt (a-1) ++ "x}" |
||||
, fx <| String.fromInt ( a - 3 ) ++ "e^x" |
||||
, fx <| String.fromInt ( a + 7 ) ++ "e^x" ++ String.fromInt a |
||||
, fx <| String.fromInt a ++ "e^x" |
||||
, fx <| String.fromInt a ++ "e^x+" ++ String.fromInt ( a + 100) |
||||
, fx <| String.fromInt ( a - 1 ) ++ "e^x+" ++ String.fromInt ( a + 100) |
||||
, fx <| String.fromInt ( a - 8 ) ++ "e^{" ++ String.fromInt (a-1) ++ "x}" ++ String.fromInt a |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Équations différentielles, equaDiff04") ] |
||||
] |
||||
|
||||
equaDiff05 param = |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: c -> equaDiff05Bis a b |
||||
|
||||
equaDiff05Bis a b = -- a positif, b négatif, pas de simplification |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $" ++ String.fromInt a ++"y'=" ++ String.fromInt b ++ "y$ ?" ] |
||||
, vr <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, vr <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Équations différentielles, equaDiff05") ] |
||||
] |
||||
|
||||
equaDiff06 param = |
||||
case param of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: c -> equaDiff06Bis a b |
||||
|
||||
equaDiff06Bis a b = -- a positif, b négatif, pas de simplification |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y" ++ String.fromInt b ++"$ ?" ] |
||||
, fx <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}" |
||||
, fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}" |
||||
, fx <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, vr <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
, fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Équations différentielles, equaDiff06") ] |
||||
] |
||||
|
||||
primitLn02 a_k = |
||||
case a_k of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: c -> primitLn02Bis a b |
||||
|
||||
primitLn02Bis a b = |
||||
let |
||||
f aa = mathTeX ( fonction ( aa ) ) |
||||
vr aa = p [] [ text ( "+" ++ ( f aa ) ) ] |
||||
fx aa = p [] [ text ( "-" ++ ( f aa ) ) ] |
||||
axpb = poly [a,b] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f <| "\\frac{" ++ String.fromInt a ++ "}{" ++ axpb ++ "}" ) ++ " ?" ] |
||||
, vr <| "\\ln\\left(" ++ axpb ++ "\\right)" |
||||
, vr <| "\\ln\\left(" ++ axpb ++ "\\right)+" ++ String.fromInt ( b + 30 ) |
||||
, vr <| "\\ln\\left(" ++ axpb ++ "\\right)" ++ String.fromInt ( a - 20) |
||||
, fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
, fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 ) |
||||
, fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
, fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 ) |
||||
, fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( a - 20) |
||||
, fx <| "\\frac{" ++ poly [a*a, a*b+a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
, fx <| "\\frac{" ++ poly [a*a, a*b-a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}" |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Primitives, Logarithme, primitLn02") ] |
||||
] |
||||
|
||||
primitPoly02 a_k = |
||||
case a_k of |
||||
[] -> div [] [] |
||||
a :: [] -> div [] [] |
||||
a :: b :: [] -> div [] [] |
||||
a :: b :: c :: [] -> div [] [] |
||||
a :: b :: c :: d :: e -> primitPoly02Bis a b c d |
||||
|
||||
primitPoly02Bis a b c d = |
||||
let |
||||
pol = [a,b,c,d,0] |
||||
polD = polyD pol |
||||
polDD = polyD polD |
||||
f a_k = mathTeX ( fonction ( poly a_k ) ) |
||||
vr a_k = p [] [ text ( "+" ++ ( f a_k ) ) ] |
||||
fx a_k = p [] [ text ( "-" ++ ( f a_k ) ) ] |
||||
in |
||||
div [] |
||||
[ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f polD ) ++ " ?" ] |
||||
, vr <| List.map2 (+) pol [0,0,0,0,5] |
||||
, vr <| List.map2 (+) pol [0,0,0,0,-8] |
||||
, vr <| List.map2 (+) pol [0,0,0,0,8] |
||||
, fx <| List.map2 (+) polD [0,0,0,8] |
||||
, fx <| List.map2 (+) polD [0,0,0,-5] |
||||
, fx <| List.map2 (+) polD [0,0,0,-8] |
||||
, fx <| List.map2 (+) polDD [0,0,8] |
||||
, fx <| List.map2 (+) polDD [0,0,-5] |
||||
, fx <| List.map2 (+) polDD [0,0,-8] |
||||
{-- |
||||
, p [] [ text ("----") ] |
||||
--} |
||||
, p [] [ text ("==== Primitives, Polynômes, primitPoly02") ] |
||||
] |
||||
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in new issue