Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{\sqrt{1+x}-1}{x}$ is gelijk aan	A. 1
B. 2
C. − 1
D. − 2
E. 0,5

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{\sqrt{1+x}-1}{x}$ is equal to	A. 1
	B. 2
	C. − 1
	D. − 2
	E. 0.5

1^ste manier :
$\\\lim_{x\to0}\frac{\sqrt{1+x}-1}{x}=\lim_{x\to0}\frac{\left(\sqrt{1+x}-1\right)\left(\sqrt{1+x}+1\right)}{x\left(\sqrt{1+x}+1\right)}\\=\lim_{x\to0}\frac{1+x-1}{x\left(\sqrt{1+x}+1\right)}=\lim_{x\to0}\frac{1}{\sqrt{1+x}+1}=\frac{1}{\sqrt1+1}=\ldots$
2^de manier :
$\\\lim_{x\to0}\frac{\sqrt{1+x}-1}{x}=\left(\frac{0}{0}\right)\buildrel H\over=\lim_{x\to0}\frac{1}{2\sqrt{1+x}}=\frac{1}{2\sqrt{1+0}}=\ldots$