Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\displaystyle \lim_{x \to 0} \frac{\sqrt{(x+1)^3}-1}{x}=$	A. 1
	B. 1.5
	C. 2
	D.
	E. $ \boldsymbol {\frac {3} {\sqrt 2}} $

$\\\displaystyle\lim_{x\to 0}\frac{\sqrt{(x+1)^3}-1}{x}=\displaystyle\lim_{x\to 0}\frac{(\sqrt{(x+1)^3}-1).(\sqrt{(x+1)^3}+1)}{x.(\sqrt{(x+1)^3}+1)}=\displaystyle\lim_{x\to 0}\frac{(x+1)^3-1}{x.(\sqrt{(x+1)^3}+1)}\\=\displaystyle\lim_{x\to 0}\frac{x^3+3x^2+3x+1-1}{x(\sqrt{(x+1)^3}+1)}=\displaystyle\lim_{x\to 0}\frac{x^2+3x+3}{\sqrt{(x+1)^3}+1}=\frac{3}{\sqrt1+1}=\frac32$

$\displaystyle \lim_{x \to 0} \frac{\sqrt{(x+1)^3}-1}{x}=$	A. 1
	B. 1,5
	C. 2
	D.
	E. \( \boldsymbol {\frac {3} {\sqrt 2}} \)