Question

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

Answer 1

Now,

$\underset{x\to 0}{lim}\frac{(x+1{)}^5-1}{x}$ $\left(\frac{0}{0}\right)$ form

Now applying L'Hospital's rule we get,

$=\underset{x\to 0}{lim}\frac{5(x+1{)}^4}{1}$

$=5$.