Chapter 12, Problem 6RE

To determine

Why does the limit not exist?

Answer to Problem 6RE

The function $\underset{x\to 2}{\lim }\frac{1}{x-2}$ does not exist.

Explanation of Solution

Given information:

With the help of the graph to find the limit (if it exists). If the limit does not exist, then explain why

  $\underset{x\to 2}{\lim }\frac{1}{x-2}$

  

Calculation:

The limit of given function is, $\underset{x\to 2}{\lim }\frac{1}{x-2}$ and its graph would be,

  

As there is a vertical asymptote at value $x=2$ the given function $\underset{x\to 2}{\lim }\frac{1}{x-2}$ does not exist.

Hence the limit of the function $\underset{x\to 2}{\lim }\frac{1}{x-2}$ does not exist.