Chapter 12, Problem 49RE

To determine

To find the limit (if it exists) by evaluating the corresponding one-sided limits.

Answer to Problem 49RE

The limit does not exist.

Explanation of Solution

Given information:

Graph the function. Determine the limit (if it exists) by evaluating the corresponding one-sided limits.

  $\underset{x\to 2}{\lim }f\left(x\right)wheref\left(x\right)=\{\begin{array}{l}5-x,x\le 2\\ x^2-3,x>2\end{array}$

Calculation:

The limit of given function is,

  $\underset{x\to 2}{\lim }f\left(x\right)wheref\left(x\right)=\{\begin{array}{l}5-x,x\le 2\\ x^2-3,x>2\end{array}$

Let plot the given function $f\left(x\right)$ .

To calculate the model graphically use graphic utility TI-83calculator,

Press Y key and enter the equation,

  

Press zoom and choose appropriate zoom function, then plot the window is as,

  

Press Trace and give $x$ value at which $y$ value need to be found.

  

From the graph we observe that the function reaches $3$ as it approaches $-2$ from right hand side function reaches $1$ as it approaches $-2$ from left hand side.

Therefore, the one sided limit is,

  $\begin{array}{l}\underset{x\to 2}{\lim }5-x=3\\ \underset{x\to 2}{\lim }{x}^2-3=1\end{array}$

Hence the limit does not exist.