Q. 66 - 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. 

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

Step-by-Step Solution

Answer

The graph of the given limit

The limit expression has the value of $\underset{x\to -1}{\lim }f\left(x\right)=2$

Step 1. Given information

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

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 0. Again for the right of $x\to -1$ the value is -1.But it has the value of 2 at $x=-1$

Therefore,the limit expression has the value of $\underset{x\to -1}{\lim }f\left(x\right)=2$