consider the function $g(x)=\begin{cases}-9,x < 11\\7,xgeq11end{cases}$. what is $lim_{x\rightarrow11}g(x)$…
consider the function $g(x)=\begin{cases}-9,x < 11\\7,xgeq11end{cases}$. what is $lim_{x\rightarrow11}g(x)$, if it exists? -9 -1 7 dne
Answer
Explanation:
Step1: Find left - hand limit
$\lim_{x\rightarrow11^{-}}g(x)=\lim_{x\rightarrow11^{-}}(-9)= - 9$
Step2: Find right - hand limit
$\lim_{x\rightarrow11^{+}}g(x)=\lim_{x\rightarrow11^{+}}7 = 7$
Step3: Check if limit exists
Since $\lim_{x\rightarrow11^{-}}g(x)\neq\lim_{x\rightarrow11^{+}}g(x)$, the limit does not exist.
Answer:
DNE