Question

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

Answer 1

Consider the given function ,

Let ,$y={lim}_{x\to 0}\frac{{(x+1)}^5}{x}$

Apply L-Hospital roll

$y={lim}_{x\to 0}\frac{\frac{d}{dx}{(x+1)}^5}{\frac{d}{dx}x}$

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

$={lim}_{x\to 0}{(x+1)}^4={(0+1)}^4$

$y=1$

This is the answer