Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 10 - Section 10.1 - Limits: Numerical and Graphical Viewpoints - Exercises - Page 699: 31c

Answer

The limit does not exist, $\displaystyle \lim_{\mathrm{x}\rightarrow 0^{+}}f(x)=+\infty$

Work Step by Step

Follow the steps in "Evaluating Limits Graphically" (step$ 4$: right limit at x=a) Tracing the right part of the graph, approaching the y-axis (x=0), we see that f(x) rises without bound. When f(x) is becoming arbitrarily large as x$\rightarrow$a, we also say that $\displaystyle \lim_{x\rightarrow a}$f(x) diverges to +$\infty$, or just $\displaystyle \lim_{\mathrm{x}\rightarrow a}f(x)$=+$\infty$. The limit does not exist, $\displaystyle \lim_{\mathrm{x}\rightarrow 0^{+}}f(x)=+\infty$
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