Question

$\underset{x\to 0}{\lim }\frac{{\sin }^{2}x}{\sqrt{2}-\sqrt{1+\cos x}}$ equals :

• A. $2\sqrt{2}$
• B. $4\sqrt{2}$
• C. $\sqrt{2}$
• D. 4

Answer 1

Answer: (B)

${\lim }_{x\to 0}\frac{\left(\frac{{\sin }^{2}x}{x^2}\right)\left(\sqrt{2}+\sqrt{1+\cos x}\right)}{\left(\frac{1-\cos x}{x^2}\right)}$
$=\frac{{\left(1\right)}^2.\left(2\sqrt{2}\right)}{\frac{1}{2}}=4\sqrt{2}$