Question

find the limit

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

Short answer

$\underset{x\to -2}{\lim }{\left(x^2+1\right)}^2=25$

Step-by-step solution

Step 1. Given information 

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

Step 2. Limit of the function 

We can find limit of a polynomial function by$\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$

As${\left(x^2+1\right)}^2$is a polynomial function and it s defined for all real numbers we can use the above formula .

$$\begin{gathered} \underset{x\to 2}{\lim }P\left(x\right)=P\left(2\right) \\ ={\left((-2{)}^2+1\right)}^2 \\ =25 \end{gathered}$$

localid="1647079279322" $$\begin{gathered} \underset{x\to 2}{\lim }P\left(x\right)=P\left(2\right) \\ ={\left((-2{)}^2+1\right)}^2 \\ =25 \end{gathered}$$