Q. 31 - Calculus

Question

Consider the graph  of the function:

Find the limits of function.

Step-by-Step Solution

Answer

The limits of the function are 2

Step 1. Given Graph

Step 2. Finding limits to the left

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

Step 3. Finding limits to the right

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

Step 4. Finding limits to the point

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