Question

$\underset{x\to 0}{lim}(\cos x{)}^{1/x^4}$

• A.
• B.
• C.
• D. limit does not exist

Answer 1

The correct option is A

$\underset{x\to 0}{lim}(\cos x{)}^{1/x^4}=e^{\underset{x\to 0}{lim}}\frac{\cos x-1}{x^4}$
$e^{\underset{x\to 0}{lim}}\frac{-2\sin \frac{x}{2}}{\frac{x}{2}}.\frac{\sin \frac{x}{2}}{\frac{x}{2}}\times \frac{1}{4x^2}=e^{-\infty }=0$