#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 Étudier sur \begin_inset Formula $\left[1;+\infty\right[$ \end_inset la fonction \begin_inset Formula $f:x\mapsto\left(x^{2}+2x\right)\ln\left(x+1\right)$ \end_inset et la représenter graphiquement dans le cadre ci-dessous. \end_layout \begin_layout Plain Layout On fera apparaitre dans ce cadre le détail des calculs, en particulier de la dérivée, et on donnera son tableau de variations en faisant apparaitre les limites éventuelles. \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 \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 "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 Représenter graphiquement sur \begin_inset Formula $\left[1;+\infty\right[$ \end_inset la fonction \begin_inset Formula $f$ \end_inset dans ce cadre. \end_layout \begin_layout Plain Layout \begin_inset VSpace 7cm \end_inset \end_layout \end_inset \end_layout \end_body \end_document