Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle \lim_{x \to +\infty}\left( \frac {\ln x} {x}+ \frac{x}{e^x} \right)$ is gelijk aan	A. 1
	B. 2
	C. e
	D. 0
	E.

[ 6-6256 - op net sinds .6.12-(E)-4.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle \lim_{x \to \infty}\left( \frac {\ln x} {x}+ \frac{x}{e^x} \right)$ is equal to	A. 1
	B. 2
	C. e
	D. 0
	E. ∞

Oplossing - Solution

$\\ \displaystyle\lim_{x\to+\infty}\left(\frac{\ln x}{x}+\frac{x}{e^x}\right)= \displaystyle\lim_{x\to+\infty}\frac{\ln x}{x}+ \displaystyle\lim_{x\to+\infty}\frac{x}{e^x}\left(=\frac{+\infty}{+\infty}+\frac{+\infty}{+\infty}\right)\\ \overset{Hospital}{=}\displaystyle\lim_{x\to+\infty}\frac{\frac1x}{1}+ \displaystyle\lim_{x\to+\infty}\frac{1}{e^x}=\frac{1}{+\infty}+\frac{1}{+\infty}=+0+0=(+)\;0$