Wiskunde Multiple Choice Vraag

$\displaystyle\lim_{\underset{>}{x\to 0}}\sqrt[x]{\frac{1+x}{1-x}}=$	A. 1
	B. e²
	C. $\large\frac{1}{e^2}$
	D. $\sqrt e$
	E.

[ 6-7389 - op net sinds 9.12.2024-(E)- ]

Translation in E N G L I S H

$\displaystyle\lim_{\underset{>}{x\to 0}}\sqrt[x]{\frac{1+x}{1-x}}=$

Oplossing - Solution

$\displaystyle\lim_{\underset{>}{x\to 0}}\sqrt[x]{\frac{1+x}{1-x}}=\displaystyle\lim_{\underset{>}{x\to 0}}\left(\frac{1+x}{1-x}\right)^\frac1x=\frac{\displaystyle\lim_{\underset{>}{x\to 0}}\:(1+x)^\frac1x}{\displaystyle\lim_{\underset{>}{x\to 0}}\:(1-x)^\frac1x}=\frac{e}{e^{-1}}=e^2$

$\displaystyle\lim_{\underset{>}{x\to 0}}\sqrt[x]{\frac{1+x}{1-x}}=$	A. 1
	B. e²
	C. \(\large\frac{1}{e^2}\)
	D. \(\sqrt e\)
	E.