Question

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

Answer 1

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

The expression takes the form $\frac{0}{0}.$

Using L hospitals Rule,

$L=\underset{x\to 0}{lim}\frac{1}{1+x}=\frac{1}{1+0}=1$