Question

graph the following function and then find the specified limit. when necessary, state that the limit does not exist. $g(x)=\

$$\begin{cases}x^{2}&\\text{for }x < 1\\\\-x + 2&\\text{for }x>1\\end{cases}$$

$. find $\lim_{x\to1}g(x)$. choose the correct graph below. find $\lim_{x\to1}g(x)$. select the correct choice below and fill in any answer boxes in your choice. a. $\lim_{x\to1}g(x)=$ (type an integer or a simplified fraction.) b. the limit does not exist

Explanation:

Step1: Find left - hand limit

For \(x\lt1\), \(G(x)=x^{2}\). So, \(\lim_{x
ightarrow1^{-}}G(x)=\lim_{x
ightarrow1^{-}}x^{2}=1^{2} = 1\).

Step2: Find right - hand limit

For \(x > 1\), \(G(x)=-x + 2\). So, \(\lim_{x
ightarrow1^{+}}G(x)=\lim_{x
ightarrow1^{+}}(-x + 2)=-1 + 2=1\).

Step3: Determine the limit

Since \(\lim_{x
ightarrow1^{-}}G(x)=\lim_{x
ightarrow1^{+}}G(x)=1\), then \(\lim_{x
ightarrow1}G(x)=1\).

Answer:

A. \(\lim_{x
ightarrow1}G(x)=1\)