Question

$\underset{x\to 0}{lim}\left[\frac{lncosx}{\sqrt[4]{41+x^2}-1}\right]\text{is equal to}$

• A. 2
• B. -2
• C. 1
• D. -1

Answer 1

The correct option is B

-2

$\underset{x\to 0}{lim}\left[\frac{Incosx}{\sqrt[4]{41+x^2}-1}\right]=\underset{x\to 0}{lim}\frac{\frac{-\sin x}{\cos x}}{\frac{1}{4}(1+x^2{)}^{\frac{-3}{4}}(2x)}\left[\text{Using L'Hospital's Rule}\right]=-2\cdot \underset{x\to 0}{lim}\frac{\tan x}{x}\cdot \underset{x\to 0}{lim}(1+x^2{)}^{\frac{3}{4}}=-2\cdot 1\cdot 1[\because \underset{x\to 0}{lim}\frac{\tan x}{x}=1]=-2$