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 698: 25f


the limit does not exist, $\displaystyle \lim_{x\rightarrow-\infty}f(x)= +\infty$

Work Step by Step

Follow the steps in "Evaluating Limits Graphically" (step 6: evaluating $\displaystyle \lim_{x\rightarrow-\infty}$f(x)) As we trace the graph to the far left , f(x) increases without bound, does not approach any particular value. 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 diverges to +$\infty,$ meaning that the limit does not exist, and $\displaystyle \lim_{x\rightarrow-\infty}f(x)= +\infty$
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