review the table of values for function g(x). what are the values of the limits? x→33+lim g(x) and x→33−lim…

review the table of values for function g(x). what are the values of the limits? x→33+lim g(x) and x→33−lim g(x)=−15 x→33+lim g(x)=−7 and x→33−lim g(x)=−16 x→33+lim g(x)=−15 and x→33−lim g(x)=−6 x→33+lim g(x)=−16 and x→33−lim g(x)=−7

review the table of values for function g(x). what are the values of the limits? x→33+lim g(x) and x→33−lim g(x)=−15 x→33+lim g(x)=−7 and x→33−lim g(x)=−16 x→33+lim g(x)=−15 and x→33−lim g(x)=−6 x→33+lim g(x)=−16 and x→33−lim g(x)=−7

Answer

Explanation:

Step1: Recall left - hand limit definition

The left - hand limit $\lim_{x\rightarrow a^{-}}g(x)$ is the value that $g(x)$ approaches as $x$ approaches $a$ from values less than $a$. Looking at the table, as $x$ approaches $33$ from values less than $33$ (e.g., $32.9,32.99,32.999$), $g(x)$ approaches $- 16$.

Step2: Recall right - hand limit definition

The right - hand limit $\lim_{x\rightarrow a^{+}}g(x)$ is the value that $g(x)$ approaches as $x$ approaches $a$ from values greater than $a$. Looking at the table, as $x$ approaches $33$ from values greater than $33$ (e.g., $33.001,33.01,33.1$), $g(x)$ approaches $-7$.

Answer:

$\lim_{x\rightarrow33^{-}}g(x)=-16$ and $\lim_{x\rightarrow33^{+}}g(x)=-7$