Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 1 - Ingredients of Change: Functions and Limits - 1.3 Activities - Page 31: 11

Answer

$$ \lim _{x \rightarrow 3^{-}}\left(\frac{1}{x-3}\right) \ \text{does not exist } $$

Work Step by Step

From the following table \begin{array}{|c|c|c|c|c|c|}\hline x\to3^- & {2.9} & {2.99} & {2.999} & {2.9999} \\ \hline \frac{1}{x-3} & {-10} & {-100} & {-1000} & {-10000} \\ \hline\end{array} This means that $$ \lim _{x \rightarrow 3^{-}}\left(\frac{1}{x-3}\right)=-\infty $$ and \begin{array}{|c|c|c|c|c|}\hline x & {3.1} & {3.01} & {3.001} & {3.0001} \\ \hline 1 / x-3 & {10} & {100} & {1000} & {10000} \\ \hline\end{array} This means that $$ \lim _{x \rightarrow 3^{+}}\left(\frac{1}{x-3}\right)=\infty $$ Hence: $$ \lim _{x \rightarrow 3^{-}}\left(\frac{1}{x-3}\right) \ \text{does not exists } $$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.