Q. 38 - Calculus

Question

Consider the graph  of the function:

Find the limits of function.

Step-by-Step Solution

Answer

The values of the given limits are 1.75,0,-2,$\infty$.

Step 1. Given graph

Step 2. Finding limits at point x=0

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{x->0}{\lim } g\left(x\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{towards} x=0 is g\left(x\right)=1.75 \\ \mathrm{Therefore},\underset{x->0}{\lim } g\left(x\right)=1.75 \end{gathered}$$

Step 3. Finding limits at point x=3

$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{limit} \mathrm{expression} \mathrm{is} \underset{x->3}{\lim } g\left(x\right) \\ \mathrm{From} \mathrm{the} \mathrm{graph}, \mathrm{the} \mathrm{functional} \mathrm{value} \mathrm{towards} x=3 is g\left(x\right)=0 \\ \mathrm{Therefore},\underset{x->3}{\lim } g\left(x\right)=0 \end{gathered}$$

Step 4. Finding limits at point x= - ∞

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

Step 5. Finding limits at point x= ∞

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