Question

lim {(x+1)^5-1}/x
x->0

​

Answer 1

Answer:

The answer is 5

Step-by-step explanation:

                  Formula to be used :

                   $\boxed{\displaystyle\lim_{x\to a}\dfrac{x^n-a^n}{x-a}=na^{n-1}}$

Given limit

                    $\displaystyle \lim_{x\to 0}\dfrac{(x+1)^5-1}{x}$

Substitute $x+1=t$ $\Rightarrow$ If $x=0$  then $t=1$

                   $=\displaystyle \lim_{t\to 1}\dfrac{t^5-1}{t-1}$

                   $=5(1)^{5-1}=5(1)^4=5(1)=5$

                    ( using above formula )