Q. 65 - Calculus

Question

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits. 

$\underset{x\to 1}{\lim }f\left(x\right),for f\left(x\right)=\left\{\begin{array}{l}{x}^2+1,if x<1\\ 3,if x=1\\ 3-x,if x>1\end{array}\right.$

Step-by-Step Solution

Answer

The graph for the given limit

The limit expression does not have any value 

Step 1. Given information

The given limit $\underset{x\to 1}{\lim }f\left(x\right),for f\left(x\right)=\left\{\begin{array}{l}{x}^2+1,if x<1\\ 3,if x=1\\ 3-x,if x>1\end{array}\right.$

Step 2. Sketch graphs by hand and use them to make approximations for the limit

The graph is drawn as below:

From the graph,we see that for the left of $x\to 1$ the value of the function is 2,Again for the right of $x\to 1$ the value is 2 

Therefore the limit expression does not have any value