the function, f(x), is plotted as shown. what values do the limits approach? lim x→2 f(x)= lim x→2− f(x)=
the function, f(x), is plotted as shown. what values do the limits approach? lim x→2 f(x)= lim x→2− f(x)=
Answer
Explanation:
Step1: Recall left - hand limit definition
The left - hand limit $\lim_{x\rightarrow2^{-}}f(x)$ is the value $f(x)$ approaches as $x$ approaches 2 from the left side. Looking at the graph, as $x$ approaches 2 from the left, $y$ approaches 3.
Step2: Recall right - hand limit definition
The right - hand limit $\lim_{x\rightarrow2^{+}}f(x)$ is the value $f(x)$ approaches as $x$ approaches 2 from the right side. Looking at the graph, as $x$ approaches 2 from the right, $y$ approaches 3.
Answer:
$\lim_{x\rightarrow2^{-}}f(x)=3$ $\lim_{x\rightarrow2^{+}}f(x)=3$