Question

Prove: ${lim}_{x\to 0}\frac{log(1+x)}{x}=1$

Answer 1

$\underset{x\to 0}{lim}\frac{log(1+x)}{x}=\frac{0}{0}$ form

using L'Hospital's rule, we get

$\Rightarrow \underset{x\to 0}{lim}\frac{1}{(1+x)\cdot 1}$

$=1$

$\therefore \underset{x\to 0}{lim}\frac{log(1+x)}{x}=1$.