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, &\text{for }x < 0\\x^{2},&\text{for }xgeq0end{cases}) find (lim_{x
ightarrow0}g(x)) choose the correct graph below. find (lim_{x
ightarrow0}g(x)). select the correct choice below and fill in any answer boxes in your choice. a. (lim_{x
ightarrow0}g(x)=) (type an integer or a simplified fraction) b. the limit does not exist

Explanation:

Step1: Find left - hand limit

For \(x<0\), \(G(x)=x\). So, \(\lim_{x
ightarrow0^{-}}G(x)=\lim_{x
ightarrow0^{-}}x = 0\).

Step2: Find right - hand limit

For \(x\geq0\), \(G(x)=x^{2}\). So, \(\lim_{x
ightarrow0^{+}}G(x)=\lim_{x
ightarrow0^{+}}x^{2}=0\).

Step3: Determine overall limit

Since \(\lim_{x
ightarrow0^{-}}G(x)=\lim_{x
ightarrow0^{+}}G(x) = 0\), then \(\lim_{x
ightarrow0}G(x)=0\).

Answer:

A. \(\lim_{x
ightarrow0}G(x)=0\)