Q. 35 - Calculus

Question

Consider the graph  of the function:

Find the limits of function.

Step-by-Step Solution

Answer

The limit is undefined.

Step 1. Given graph

Step 2. Finding limits to the left x=-1

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is}: \underset{x->1^{-}}{\lim } g\left(x\right) \\ F\mathrm{rom} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{o}f x=-1 is g\left(x\right)= \infty \\ \mathrm{Therefore}, \underset{\mathrm{x}->1^{-}}{\lim } g\left(x\right) =\infty \end{gathered}$$

Step 3. Finding limits to the right x=-1

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is}: \underset{x->1^{+}}{\lim } g\left(x\right) \\ F\mathrm{rom} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{o}f x=-1 is g\left(x\right)= -\infty \\ \mathrm{Therefore}, \underset{\mathrm{x}->1^{+}}{\lim } g\left(x\right) =-\infty \end{gathered}$$

Step 4. Finding limits to the point

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is}: \underset{x->1}{\lim } g\left(x\right) \\ F\mathrm{rom} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{o}f x=-1 is g\left(x\right)= no value \\ \mathrm{Therefore}, \underset{\mathrm{x}->1^{}}{\lim } g\left(x\right) =\mathrm{no} \mathrm{value} \\ \mathrm{hence} \mathrm{the} \mathrm{limit} \mathrm{is} \mathrm{undefined} \end{gathered}$$