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Infinite Limits

    A function infinite limits _gr_1.gif] that increases without bound as infinite limits _gr_2.gif] approaches infinite limits _gr_3.gif] is said to tend to infinity at infinite limits _gr_4.gif] and is denoted by

infinite limits _gr_5.gif]

Similarly, a function infinite limits _gr_6.gif] that decreases without bound as infinite limits _gr_7.gif] approaches infinite limits _gr_8.gif] is said to tend to infinity at infinite limits _gr_9.gif] and is denoted by

infinite limits _gr_10.gif]

Example (Infinite Limits) Determine infinite limits _gr_11.gif]

    Solution. Since infinite limits _gr_12.gif] increases without bound as infinite limits _gr_13.gif] and   infinite limits _gr_14.gif] increases without bound as infinite limits _gr_15.gif] we say that infinite limits _gr_16.gif]

infinite limits _gr_17.gif]

infinite limits _gr_18.gif]

Example (Infinite Limits) Determine infinite limits _gr_19.gif]

    Solution. Since infinite limits _gr_20.gif] decreases without bound as infinite limits _gr_21.gif] and   infinite limits _gr_22.gif] increases without bound as infinite limits _gr_23.gif] we say that infinite limits _gr_24.gif] does not exist.

infinite limits _gr_25.gif]
infinite limits _gr_26.gif]

Cite this as:
Infinite Limits
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/infinite-limits.html
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