Question

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

Solve :

Answer 1

As $log1=0\Rightarrow$ it is $\frac{0}{0}$ form,

Applying l' opital,

${lim}_{x\to 0}\frac{\left(\frac{1}{1+\alpha x}\right)\alpha }{1}=\alpha$