Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle \lim_{x \to \pm \infty}\left ( \frac{x\,+\,6}{x} \right )^{3x}$ is gelijk aan	A. 1
	B. e²
	C. e³
	D. e¹⁸
	E.

[ 5,6-3711 - op net sinds 11.7.05-(E)-30.10.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle \lim_{x \to \infty}\left ( \frac{x\,+\,6}{x} \right )^{3x}$ is equal to	A. 1
	B. e²
	C. e³
	D. e¹⁸
	E. ∞

Oplossing - Solution

$\lim_{x\to\pm\infty }\: \left( \frac{x+6}{x} \right)^{\!3x}= \lim_{x\to\pm\infty }\: \left(\! 1+\frac{6}{x} \right)^{\frac x6.18}= \left [\lim_{x\to\pm\infty }\left(\! 1+\frac{6}{x} \right)^{\frac x6} \right ]^{18}=e^{18}$