Question

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

Answer 1

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

Using $L^{\prime }Hospital$ we get,

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