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diff --git a/macros/latex/contrib/alterqcm/examples/latex/AntillesESjuin2006.tex b/macros/latex/contrib/alterqcm/examples/latex/AntillesESjuin2006.tex new file mode 100644 index 0000000000..0a7203e926 --- /dev/null +++ b/macros/latex/contrib/alterqcm/examples/latex/AntillesESjuin2006.tex @@ -0,0 +1,77 @@ +\documentclass[11pt]{article} +\usepackage{xkeyval,array,multirow,amsmath,amssymb} +\usepackage{fullpage,longtable} +\usepackage[english]{alterqcm} +\usepackage[english]{babel} + +\begin{document} +\begin{alterqcm}[lq=90mm,pre=true,long] + +\AQquestion{Among the following propositions, which one allows to affirm that the exponential function admits for asymptote the equation line $y = 0$?} +{{$\displaystyle\lim_{x \to +\infty} \text{e}^x = + \infty$}, +{$\displaystyle\lim_{x \to -\infty} \text{e}^x = 0$}, +{$\displaystyle\lim_{x \to +\infty} \dfrac{\text{e}^x}{x} = + \infty$}} + +\AQquestion{Among the following propositions, which is the one that allows to affirm that the inequation $\ln (2x + 1) \geqslant \ln (x + 3)$ admits the interval $\big[2~;~+\infty\big[$ as a set of solution? } +{{\begin{minipage}{5cm}the ln function is positive on $\big[1~;~+\infty\big[$\end{minipage}}, +{$\displaystyle\lim_{x \to +\infty} \ln x = + \infty$}, +{\begin{minipage}{5cm}the $\ln$ function is increasing on $\big]0~;~+\infty\big[$\end{minipage}} +} + +\AQquestion{Among the following propositions, which one allows us to assert that a primitive of the function $f$ defined on $\mathbb{R}$ by $x \mapsto (x + 1)\text{e}^x$ is the function $g~:~x~ \mapsto~ x~ \text{e}^x$~? } +{{for all real $x,~f'(x) = g(x)$}, +{for all real $x,~g'(x) = f(x)$}, +{\begin{minipage}{5.5cm} for all real $x,~g(x) = f'(x) + k$, $k$ some kind of real \end{minipage}}} + +\AQquestion[pq=2mm]{ The equation $2\text{e}^{2x} - 3\text{e}^x + 1 = $0 admits for set solution} +{{$\left\{\dfrac{1}{2}~;~1\right\}$}, +{$\left\{0~;~\ln \dfrac{1}{2}\right\}$}, +{$\big\{0~;~\ln 2\big\}$} +} + +\AQquestion[pq=2mm]{For all $n \in \mathbb{N}$ } +{{$\displaystyle\lim_{x \to +\infty} \frac{\text{e}^x}{x^n} = 1$}, +{$\displaystyle\lim_{x \to +\infty} \frac{\text{e}^x}{x^n} = +\infty$}, +{$\displaystyle\lim_{x \to +\infty} \frac{\text{e}^x}{x^n} = 0$}} + +\AQquestion[pq=1pt]{Let $f$ be the function set to $\big]0~;~+\infty\big[$ par $f(x) = 2\ln x - 3x + 4$. In a benchmark, an equation of the tangent to the curve representing $f$ at abscissa point 1 is :} +{{$y = - x + 2$}, +{$y = x + 2$}, +{$y = - x - 2$} +} + +\AQquestion[pq=2mm]{The mean value over $\big[1; 3\big]$ of the $f$ function defined by : $f(x) = x^2 + 2x$ is:} +{{$\dfrac{50}{3}$}, +{$\dfrac{25}{3}$}, +{$6$} +} +\AQquestion{ exp$(\ln x) = x$ for any $x$ belonging to } +{{$\mathbb{R}$}, +{$\big]0~;~+ \infty\big[$}, +{$\big[0~;~+\infty\big[$} +} +\AQquestion[pq=1pt]{Let $f$ be the function set to $\big]0~;~+\infty\big [$ per $f(x) = 2\ln x - 3x + 4$. In a benchmark, an equation of the tangent to the curve representing $f$ at abscissa point 1 is :} +{{$y = - x + 2$}, +{$y = x + 2$}, +{$y = - x - 2$} +} + +\AQquestion[pq=2mm]{The mean value over $\big[1; 3\big]$ of the $f$ function defined by : $f(x) = x^2 + 2x$ is:} +{{$\dfrac{50}{3}$}, +{$\dfrac{25}{3}$}, +{$6$} +} +\AQquestion{ exp$(\ln x) = x$ for any $x$ belonging to } +{{$\mathbb{R}$}, +{$\big]0~;~+ \infty\big[$}, +{$\big[0~;~+\infty\big[$} +} +\end{alterqcm} +\end{document} + +% AntillesESjuin2006 + +% encoding : utf8 +% format : pdflatex +% engine : pdfetex +% author : Alain Matthes
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