Q. 37 - Calculus

Question

Consider the graph  of the function:

Find the limits of function.

Step-by-Step Solution

Answer

The limit is 2.

Step 1. Given graph

Step 2. Finding value to the left x=2

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{\mathrm{x}->2^{-}}{\lim } \mathrm{g}\left(\mathrm{x}\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{of} x=2 is g\left(x\right)=-1 \\ \mathrm{Therefore},\underset{\mathrm{x}->2^{-}}{\lim } \mathrm{g}\left(\mathrm{x}\right) =-1 \end{gathered}$$

Step 3.. Finding value to the right x=2

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{\mathrm{x}->2^{+}}{\lim } \mathrm{g}\left(\mathrm{x}\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} right\mathrm{of} x=2 is g\left(x\right)=-1 \\ \mathrm{Therefore},\underset{\mathrm{x}->2^{+}}{\lim } \mathrm{g}\left(\mathrm{x}\right) =-1 \end{gathered}$$

Step 4. . Finding value to the point x=2

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{\mathrm{x}->2^{}}{\lim } \mathrm{g}\left(\mathrm{x}\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{to} \mathrm{the} \mathrm{left} \mathrm{of} x=2 is g\left(x\right)=-1 \\ \mathrm{Therefore},\underset{\mathrm{x}->2}{\lim } \mathrm{g}\left(\mathrm{x}\right) =-1 \\ \mathrm{Hence} \mathrm{the} \mathrm{value} \mathrm{is} g\left(2\right)=-2 \end{gathered}$$