Chapter 12, Problem 31CLT

To determine

Find the limit (if it exists).

Answer to Problem 31CLT

Limit does not exist.

Explanation of Solution

Given information:

Find the limit (if it exists). If the limit does not exist, then explain why. Use a graphing utility to verify your result graphically.

  $\underset{x\to 0}{\lim }sin\left(\frac{\pi }{x}\right)$

Calculation:

Consider the given limit.

  $\underset{x\to 0}{\lim }sin\left(\frac{\pi }{x}\right)$

Now identify the function,

  $\begin{array}{l}f\left(x\right)=sin\left(\frac{\pi }{x}\right)\\ when\\ x\to 0\end{array}$

The limit does not exist because the function approaches two different values.

Plot the function by using $TI-83$ graphic calculator,

Press Y= and enter the function.

  

Press window to choose the proper scale.

  

Now press GRAPH and display will be.

  

Hence the limit does not exist because the function approaches two different values.