Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises - Page 93: 21

Answer

$\lim\limits_{t \to 0}\dfrac{e^{5t}-1}{t}$ We could guess that the value of the limit is $5.0$.

Work Step by Step

$\lim\limits_{t \to 0}\frac{e^{5t}-1}{t}$ We can evaluate the function at the given numbers: $t = 0.5$: $\frac{e^{5(0.5)}~-1}{0.5} = 22.364988$ $t = -0.5$: $\frac{e^{5(-0.5)}~-1}{-0.5} = 1.835830$ $t = 0.1$: $\frac{e^{5(0.1)}~-1}{0.1} = 6.487213$ $t = -0.1$: $\frac{e^{5(-0.1)}~-1}{-0.1} = 3.934693$ $t = 0.01$: $\frac{e^{5(0.01)}~-1}{0.01} = 5.127110$ $t = -0.01$: $\frac{e^{5(-0.01)}~-1}{-0.01} = 4.877058$ $t = 0.001$: $\frac{e^{5(0.001)}~-1}{0.001} = 5.012521$ $t = -0.001$: $\frac{e^{5(-0.001)}~-1}{-0.001} = 4.987521$ $t = 0.0001$: $\frac{e^{5(0.0001)}~-1}{0.0001} = 5.001250$ $t = -0.0001$: $\frac{e^{5(-0.0001)}~-1}{-0.0001} = 4.998750$ We could guess that the value of the limit is $5.0$
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