University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Section 2.2 - Limit of a Function and Limit Laws - Exercises - Page 68: 76

Answer

$f(x)$ appears to have a limit as $x\to0$, which is $1.098612...$
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Work Step by Step

$$f(x)=\frac{3^x-1}{x}$$ (a) The table is shown below. As we can see from 2 tables below, as $x$ gets more decimals and approaches $0$, the value of $f(x)$ also gets more decimals and apparently approaches a value of $1.098612...$ from both sides. Even though, we cannot get an exact value of this number, f(x) still approaches this same value either from the left or the right side as $x\to0$, meaning $f(x)$ appears to have a limit here, which is $1.098612...$ (b) The graph is shown below. Looking at the graph, we confirm that the closer $x$ approaches $0$, the closer $f(x)$ gets to $1.098612...$.
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