44 lines
890 B
TeX
44 lines
890 B
TeX
\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Limites de fonctions - Cours}
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\date{Mai 2021}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\setcounter{section}{3}
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\section{Limites comparés entre polynômes et exponentielle}
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\begin{propriete}
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Soit $n$ un entier naturel alors
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\[
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\lim_{x\rightarrow +\infty} \frac{e^x}{x^n} = +\infty
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\]
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\[
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\lim_{x\rightarrow +\infty} \frac{x^n}{e^x} = \lim_{x\rightarrow +\infty} x^n e^{-x} = 0
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\]
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\end{propriete}
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\paragraph{Exemples} Calculs de limites
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\begin{multicols}{2}
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$\ds \lim_{x\rightarrow +\infty} \frac{e^x}{x^2} = $
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$\ds \lim_{x\rightarrow +\infty} x^4 e^{-x} = $
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\columnbreak
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$\ds \lim_{x\rightarrow +\infty} \frac{e^x}{x^3 + 3x +1} = $
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$\ds \lim_{x\rightarrow +\infty} (x^5 + 2x^4)e^{-x} = $
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\end{multicols}
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\end{document}
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