Question

Solve:
$\underset{x\to 0}{lim}\frac{e^x-x-1}{x-5}=$

Answer 1

$\underset{x\to 0}{lim}\frac{e^x-x-1}{x-5}=\frac{e^o-0-1}{0-5}$

$=\frac{1-1}{-5}$ [Since, $a^0=1$ for any $a\ne 0$]

$=\frac{0}{-5}$.
$\therefore \underset{x\to 0}{lim}\frac{e^x-x-1}{x-5}=0$