Chapter 13, Problem 1RE

In Problems $1-11$, find the limit.

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

To determine

To calculate: The value of $\underset{x\to 2}{\lim }(3x^2-2x+1)$.

Answer to Problem 1RE

Solution:

The value of $\underset{x\to 2}{\lim }(3x^2-2x+1)$ is $9$.

Explanation of Solution

Given information:

The expression, $\underset{x\to 2}{\lim }(3x^2-2x+1)$

Formula used:

If $P$ is polynomial function, then $\underset{x\to c}{\lim }P\left(x\right)=P\left(c\right)$ for any number $c$

Calculation:

As $P\left(x\right)=3x^2-2x+1$ is a polynomial then $\underset{x\to 2}{\lim }P\left(x\right)=P\left(2\right)$,

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

$\underset{x\to 2}{\lim }(3x^2-2x+1)=12-4+1=9$,

Hence, the value of $\underset{x\to 2}{\lim }(3x^2-2x+1)$ is $9$.