graph the following function and then find the specified limit. when necessary, state that the limit does…
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\rightarrow0}g(x)) choose the correct graph below. find (lim_{x\rightarrow0}g(x)). select the correct choice below and fill in any answer boxes in your choice. a. (lim_{x\rightarrow0}g(x)=) (type an integer or a simplified fraction) b. the limit does not exist
Answer
Explanation:
Step1: Find left - hand limit
For (x<0), (G(x)=x). So, (\lim_{x\rightarrow0^{-}}G(x)=\lim_{x\rightarrow0^{-}}x = 0).
Step2: Find right - hand limit
For (x\geq0), (G(x)=x^{2}). So, (\lim_{x\rightarrow0^{+}}G(x)=\lim_{x\rightarrow0^{+}}x^{2}=0).
Step3: Determine overall limit
Since (\lim_{x\rightarrow0^{-}}G(x)=\lim_{x\rightarrow0^{+}}G(x) = 0), then (\lim_{x\rightarrow0}G(x)=0).
Answer:
A. (\lim_{x\rightarrow0}G(x)=0)