Question

In Problems 7– 42, find each limit algebraically.

$\underset{x\to 1}{\lim }{\left(x^2+1\right)}^3$

Short answer

The answer is 8.

Step-by-step solution

Step. 1 Given Information

Given is the limit on which x tends to 1 and the function given is:

${\left(x^2+1\right)}^3$

Step. 2 Solving the limit

Firstly, we check whether the given function is in indeterminant form or not.

Since if we put $x=1$then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function. So,

$$\begin{gathered} \underset{x\to 1}{\lim }{\left(x^2+1\right)}^3={\left(1^2+1\right)}^3 \\ =2^3=8. \end{gathered}$$