Question

Solve: $\underset{x\to 0}{lim}\frac{(x+1{)}^5-1}{x}$

Answer 1

$Wehave$

$I={lim}_{x\to 0}\frac{{\left(x+1\right)}^5-1}{x}$

Using L-hospital rule

$I={lim}_{x\to 0}\frac{{5\left(x+1\right)}^4-0}{1}$

$=5(0+1{)}^4=5$