Question

find the limit

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

Short answer

$\underset{x\to 2}{\lim }\left(3x^2-2x+1\right)=9$

Step-by-step solution

Step 1. Given information

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

Step 2. Limit of the function 

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

As f(x)= $\left(3x^2-2x+1\right)$is a polynomial function and it s defined for all real numbers we can use the above formula.

$$\begin{gathered} \underset{x\to 2}{\lim }P\left(x\right)=P\left(2\right) \\ =3(2{)}^2-2(2)+1 \\ =9 \end{gathered}$$