62 lines
1.4 KiB
TeX
62 lines
1.4 KiB
TeX
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\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{avril 2021}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\setcounter{section}{1}
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\section{Limites de polynômes}
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\begin{propriete}[Limites des monômes]
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\begin{center}
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\begin{tabular}{|l|*{2}{c|}}
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\hline
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$\ds \lim_{x\rightarrow ...} x^n = $ & $n$ paire & $n$ impaire\\
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\hline
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$+\infty$ & $+\infty$ & $+\infty$ \\
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\hline
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$-\infty$ & $+\infty$ & $-\infty$ \\
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\hline
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\end{tabular}
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\end{center}
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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} x^2 = $
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$\ds \lim_{x\rightarrow -\infty} x^4 = $
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$\ds \lim_{x\rightarrow +\infty} -5x^2 = $
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\columnbreak
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$\ds \lim_{x\rightarrow +\infty} x^3 = $
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$\ds \lim_{x\rightarrow -\infty} x^5 = $
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$\ds \lim_{x\rightarrow -\infty} -2x^3 = $
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\end{multicols}
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\afaire{Calculer les limites}
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\begin{propriete}[Simplification des limites de polynôme]
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La limite en $+\infty$ et $-\infty$ d'un polynôme est égale à la limite de son monôme de plus haut degré
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\end{propriete}
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\paragraph{Exemple} Calculs des limites
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\begin{multicols}{2}
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$\ds \lim_{x\rightarrow +\infty} x^2 - 3x + 1 = $
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\columnbreak
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$\ds \lim_{x\rightarrow -\infty} -2x^3 + 10x^2 - 100 = $
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\end{multicols}
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\end{document}
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