Question

Evaluate the following limits
$\underset{x\to 0}{lim}\left(\frac{e^x-\sin x}{x}\right)$

Answer 1

Solution

$\underset{x\to 0}{lim}\left(\frac{e^x-\sin x}{x}\right)$

Value of numerator at $x=0$

$e^o-\sin o=1-0=1$

value of denominator at $x=0$

$x=0$

This is $\frac{1}{0}$ is determinate form

So limit does not exist.