Wiskunde Multiple Choice Vraag

$\inline\\\displaystyle\lim_{x\to+\infty}\left[\:x\left(1-\sqrt[x]{2}\right)\,\right]=$	A. 1
B. log 2
C. − log 2
D. ln 2
E. − ln 2

$\inline\\\displaystyle\lim_{x\to+\infty}\left[\:x\left(1-\sqrt[x]{2}\right)\,\right]=$

$\inline\\\displaystyle\lim_{x\to+\infty}\left[\:x\left(1-\sqrt[x]{2}\right)\,\right]=\lim_{x\to+\infty}\frac{1-\sqrt[x]{2}}{\frac1x}\left(=\frac00\right)\\\overset{H}{=}\lim_{x\to+\infty}\frac{-2^{\frac1x}.(-\frac{1}{x^2}).\ln 2}{-\frac{1}{x^2}}=-\ln 2\lim_{x\to+\infty}2^{\frac1x}=-\ln 2.(2^0)=-\ln 2$
( ≈ 0,6333)

^{gricha - vA161 - 30.3.2026}