University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 2 - Additional and Advanced Exercises - Page 112: 1

Answer

a) As $x$ approaches $0$, $x^x$ approaches $1$. b) The graph heads for the value $1$ on the $y$-axis.
1537340913

Work Step by Step

a) Using the calculator to calculate $x^x$ for $x=0.1, 0.01, 0.001$ and so on: - For $x=0.1$: $x^x\approx0.794328$ - For $x=0.01$: $x^x\approx0.954993$ - For $x=0.001$: $x^x\approx0.993116$ - For $x=0.0001$: $x^x\approx0.999079$ - For $x=0.00001$: $x^x\approx0.999885$ - For $x=0.000001$: $x^x\approx0.999986$ - For $x=0.0000001$: $x^x\approx0.999998$ We can easily see the pattern here is that as $x$ gets smaller and approaches $0$, $x^x$ approaches $1$. b) The graph of the function $y=x^x$ is included below. Looking at the graph, it seems to head for the value $1$ on the $y$-axis.
Small 1537340913
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.