Question

$\lim_{x\to \ 0 } \frac{\sqrt{1+x}- \sqrt{1-x}}{x}$

Answer 1

Rationalizam sus cu conjugata lui care este $\sqrt{1+x}+ \sqrt{1-x}$
si avem :$\lim_{x \to \00} \frac{1+x-1+x}{x( \sqrt{1+x}+ \sqrt{1-x}) }=\lim_{x \to \00} \frac{2x}{x( \sqrt{1+x}+ \sqrt{1-x}) }=\lim_{x \to \00} \frac{2}{( \sqrt{1+x}+ \sqrt{1-x}) }$=2/2=1
Sper ca ai inteles, bafta!