Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to +\infty} \: {\frac{x}{x-\sqrt{1+x}}}$ is gelijk aan	A. 1
B. 2
C. −1
D. 0
E.

$\displaystyle \lim_{x \to \infty} \: {\frac{x}{x-\sqrt{1+x}}}$ is equal to	A. 1
	B. 2
	C. -1
	D. 0
	E. ∞

$\\\displaystyle\lim_{x\to+\infty}\:{\frac{x}{x-\sqrt{1+x}}}=\displaystyle\lim_{x\to+\infty}\:\frac{x}{x-\sqrt{\frac{x^2}{x^2}+\frac{x^2}{x}}}=\displaystyle\lim_{x\to+\infty}\:\frac{x}{x-\sqrt{x^2(\frac{1}{x^2}+\frac1x)}}=\displaystyle\lim_{x\to+\infty}\:\frac{x}{x-x\sqrt{\frac{1}{x^2}+\frac1x}}=\displaystyle\lim_{x\to+\infty}\:\frac{x}{1-\sqrt{\frac{1}{x^2}+\frac1x}}=\frac{1}{1-0}=1$