Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\displaystyle \lim_{x\to2}\frac{\sqrt{x^3+1}-3}{x^2-2x}=$	A. 1
B. \(\frac12\)
C. \(\frac13\)
D. \(\frac43\)
E. 0

$\displaystyle \lim_{x\to2}\frac{\sqrt{x^3+1}-3}{x^2-2x}\left(=\frac00\right)=\lim_{x\to2}\frac{x^3+1-9}{(x^2-2x)(\sqrt{x^3+1}+3)}\\=\lim_{x\to2}\frac{x^3-8}{x(x-2)(\sqrt{x^3+1}+3)}==\lim_{x\to2}\frac{(x-2)(x^2+2x+4)}{x(x-2)(\sqrt{x^3+1}+3)}\\=\lim_{x\to2}\frac{x^2+2x+4}{x(\sqrt{x^3+1}+3)}=\frac{4+4+4}{2(3+3)}=\frac{12}{12}=1 \qquad\qquad$