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TheAprendiz @TheAprendiz

November 2019 1 40 Report

$\lim_{x \to +\infty} \ xe^{-x}$

$\lim_{x \to \infty} \frac{ln x}{x}$

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Comentários (1) Vamos aplicar a regra de Cauchy:

1 -

$\displaystyle \lim_{x \to +\infty} x \cdot e^{-x} \\ \\ \\ \lim_{x \to +\infty} x \cdot \frac{1}{e^{x}} \\ \\ \\ \lim_{x \to +\infty} \frac{x}{e^{x}} \\ \\ \\ \lim_{x \to +\infty} \frac{1}{e^{x}} \\ \\ \\ \lim_{x \to +\infty} \frac{1}{e^{\infty}} = 0$

2 -

$\displaystyle \lim_{x \to +\infty} \frac{\ln(x)}{x} \\ \\ \\ \lim_{x \to +\infty} \frac{\displaystyle \frac{1}{x}}{1} \\ \\ \\ \lim_{x \to +\infty} \frac{1}{x} \\ \\ \\ \lim_{x \to +\infty} \frac{1}{\infty} = 0$

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