Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle\: \lim_{x \to +\infty}\: \frac{x^x}{{(x-1)^x}$ is gelijk aan	A. 1
	B. e
	C.
	D. 0
	E.

[ 6-2607 - op net sinds 17.7.12-(E)-30.10.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle\: \lim_{x \to \infty}\: \frac{x^x}{{(x-1)^x}$ is equal to	A. 1
	B. e
	C.
	D. 0
	E. ∞

Oplossing - Solution

$\large {\color{DarkGreen} \lim_{x \to +\infty}\frac{x^x}{(x-1)^x}= \lim_{x \to +\infty}\left ( \frac{x}{x-1} \right )^x= \lim_{x \to +\infty}\left ( \frac{x-1}{x} \right )^{-x} \lim_{x \to +\infty}\left ( 1+\frac{1}{-x} \right )^{-x}=e }$