Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.2 Exercises - Page 57: 56

Answer

(a) Please see the graph. (b) $$\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 3 & 3.3 & 3.4 & 3.5 & 3.6 & 3.7 & 4 \\ \hline C & 7.77 & 8.76 & 8.76 & 8.76 & 8.76 & 8.76 & 8.76 \\ \hline \end{array}$$ (c) $$\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 2 & 2.5 & 2.9 & 3 & 3.1 & 3.5 & 4 \\ \hline C & 6.78 & 7.77 & 7.77 & 7.77 & 8.76 & 8.76 & 8.76 \\ \hline \end{array}$$

Work Step by Step

(b) Looking at the graph and table, we find that as $x$ approaches $3.5$ from the left and right, the function $C(t)$ approaches $8.76$. Thus, we can conclude that$$\lim_{x \to 3.5} C(t)= 8.76 \, .$$ (c) Looking at the graph and table, we find that as $x$ approaches $3$ from the left and right, the function $C(t)$ approaches $7.77$ and $8.76$, respectively. Thus, we can conclude that $\lim_{x \to 3} C(t)$ does not exist.
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