Q. 36 - Calculus

Question

Consider the graph  of the function:

Find the limits of function.

Step-by-Step Solution

Answer

The limit is 0.

Step 1. Given graph

Step 2. Finding limits to the left x=1

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{x->1^{-}}{\lim } g\left(x\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{of} x=1 is g\left(x\right)=0 \\ \mathrm{Therefore},\underset{x->1^{-}}{\lim } g\left(x\right) =0 \end{gathered}$$

Step 3. Finding limits to the right x=1

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{x->1^{+}}{\lim } g\left(x\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{of} x=1 is g\left(x\right)=0 \\ \mathrm{Therefore},\underset{x->1^{+}}{\lim } g\left(x\right) =0 \end{gathered}$$

Step 4. Finding limits to the point x=1

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{x->1^{}}{\lim } g\left(x\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{of} x=1 is g\left(x\right)=0 \\ \mathrm{Therefore},\underset{x->1^{}}{\lim } g\left(x\right) =0 \\ \mathrm{Hence} \mathrm{limit} \mathrm{is} 0. \end{gathered}$$