You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
354 lines
5.1 KiB
354 lines
5.1 KiB
#LyX 2.3 created this file. For more info see http://www.lyx.org/
|
|
\lyxformat 544
|
|
\begin_document
|
|
\begin_header
|
|
\save_transient_properties true
|
|
\origin unavailable
|
|
\textclass article
|
|
\use_default_options true
|
|
\maintain_unincluded_children false
|
|
\language french
|
|
\language_package default
|
|
\inputencoding auto
|
|
\fontencoding global
|
|
\font_roman "default" "default"
|
|
\font_sans "default" "default"
|
|
\font_typewriter "default" "default"
|
|
\font_math "auto" "auto"
|
|
\font_default_family default
|
|
\use_non_tex_fonts false
|
|
\font_sc false
|
|
\font_osf false
|
|
\font_sf_scale 100 100
|
|
\font_tt_scale 100 100
|
|
\use_microtype false
|
|
\use_dash_ligatures true
|
|
\graphics default
|
|
\default_output_format default
|
|
\output_sync 0
|
|
\bibtex_command default
|
|
\index_command default
|
|
\paperfontsize default
|
|
\spacing single
|
|
\use_hyperref false
|
|
\papersize default
|
|
\use_geometry true
|
|
\use_package amsmath 1
|
|
\use_package amssymb 1
|
|
\use_package cancel 1
|
|
\use_package esint 1
|
|
\use_package mathdots 1
|
|
\use_package mathtools 1
|
|
\use_package mhchem 1
|
|
\use_package stackrel 1
|
|
\use_package stmaryrd 1
|
|
\use_package undertilde 1
|
|
\cite_engine basic
|
|
\cite_engine_type default
|
|
\biblio_style plain
|
|
\use_bibtopic false
|
|
\use_indices false
|
|
\paperorientation portrait
|
|
\suppress_date false
|
|
\justification true
|
|
\use_refstyle 1
|
|
\use_minted 0
|
|
\index Index
|
|
\shortcut idx
|
|
\color #008000
|
|
\end_index
|
|
\leftmargin 5mm
|
|
\topmargin 2cm
|
|
\rightmargin 5mm
|
|
\bottommargin 5mm
|
|
\secnumdepth 3
|
|
\tocdepth 3
|
|
\paragraph_separation indent
|
|
\paragraph_indentation default
|
|
\is_math_indent 0
|
|
\math_numbering_side default
|
|
\quotes_style french
|
|
\dynamic_quotes 0
|
|
\papercolumns 1
|
|
\papersides 1
|
|
\paperpagestyle empty
|
|
\tracking_changes false
|
|
\output_changes false
|
|
\html_math_output 0
|
|
\html_css_as_file 0
|
|
\html_be_strict false
|
|
\end_header
|
|
|
|
\begin_body
|
|
|
|
\begin_layout Standard
|
|
\begin_inset ERT
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
|
\backslash
|
|
null
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset VSpace vfill
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Box Boxed
|
|
position "t"
|
|
hor_pos "c"
|
|
has_inner_box 1
|
|
inner_pos "t"
|
|
use_parbox 0
|
|
use_makebox 0
|
|
width "65col%"
|
|
special "none"
|
|
height "1in"
|
|
height_special "totalheight"
|
|
thickness "0.4pt"
|
|
separation "3pt"
|
|
shadowsize "4pt"
|
|
framecolor "black"
|
|
backgroundcolor "none"
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset VSpace 1cm
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
Soit la suite
|
|
\begin_inset Formula $u$
|
|
\end_inset
|
|
|
|
telle que
|
|
\begin_inset Formula $u_{0}=2$
|
|
\end_inset
|
|
|
|
et
|
|
\begin_inset Formula $u_{n+1}=5u_{n}+4$
|
|
\end_inset
|
|
|
|
pour tout entier
|
|
\begin_inset Formula $n\geqslant1$
|
|
\end_inset
|
|
|
|
, et soit
|
|
\begin_inset Formula $v$
|
|
\end_inset
|
|
|
|
la suite définie par
|
|
\begin_inset Formula $v_{n}=u_{n}+1$
|
|
\end_inset
|
|
|
|
pour tout entier
|
|
\begin_inset Formula $n\geqslant1$
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
Montrer que la suite
|
|
\begin_inset Formula $v$
|
|
\end_inset
|
|
|
|
est une suite géométrique dont on donnera la raison et le premier terme
|
|
puis donner une formule pour
|
|
\begin_inset Formula $v_{n}$
|
|
\end_inset
|
|
|
|
puis pour
|
|
\begin_inset Formula $u_{n}$
|
|
\end_inset
|
|
|
|
en fonction de l'entier naturel
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset VSpace 1cm
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset ERT
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset VSpace 5mm
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Box Boxed
|
|
position "t"
|
|
hor_pos "c"
|
|
has_inner_box 1
|
|
inner_pos "t"
|
|
use_parbox 0
|
|
use_makebox 0
|
|
width "100col%"
|
|
special "none"
|
|
height "1in"
|
|
height_special "totalheight"
|
|
thickness "0.4pt"
|
|
separation "3pt"
|
|
shadowsize "4pt"
|
|
framecolor "black"
|
|
backgroundcolor "none"
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset VSpace 1cm
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
Établir, en faisant apparaitre les calculs, le tableau de signe sur
|
|
\begin_inset Formula $\mathbb{R}$
|
|
\end_inset
|
|
|
|
de la fonction
|
|
\begin_inset Formula $f:x\mapsto3x^{2}+4x-7$
|
|
\end_inset
|
|
|
|
et en déduire les solutions sur
|
|
\begin_inset Formula $\mathbb{R}$
|
|
\end_inset
|
|
|
|
de l'inéquation
|
|
\begin_inset Formula $3x^{2}+4x+8\leqslant15$
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
(Si vous ne parvenez pas à le faire par le calcul, une résolution graphique
|
|
du problème rapportera une partie des points)
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset VSpace 1cm
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset ERT
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\backslash
|
|
hrule
|
|
\backslash
|
|
vspace{8mm}
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|
|
|