Wiskunde Multiple Choice Vraag

$\displaystyle \lim_{x\to0}\frac{\sqrt{1-x^2}-\sqrt{1+x^2}}{2x^2}=$	A. 0
B. 1
C. 2
D. \(\boldsymbol{\frac12}\)
E. \(\boldsymbol{-\frac12}\)

IN CONS IN CONSTR IN CONSTRUC IN CONSTRUCTI IN CONSTRUCTION	A.
	B.
	C.
	D.
	E.

$\inline\displaystyle \lim_{x\to0}\frac{\sqrt{1-x^2}-\sqrt{1+x^2}}{2x^2}\\=\lim_{x\to0}\frac{(\sqrt{1-x^2}-\sqrt{1+x^2})(\sqrt{1-x^2}+\sqrt{1+x^2})}{(2x^2)(\sqrt{1-x^2}+\sqrt{1+x^2})}=\\=\lim_{x\to0}\frac{1-x^2-1-x^2}{(2x^2)(\sqrt{1-x^2}+\sqrt{1+x^2})}\\=\lim_{x\to0}\frac{-1}{\sqrt{1-x^2}+\sqrt{1+x^2}}=\frac{-1}{\sqrt{1}+\sqrt{1}}=-\frac12$