How does the vertical asymptotes affect limits at infinity?

1 Answer
Jim H
Mar 13, 2015

Vertical asymptotes and limits at infinity do not affect each other.

Being a bit careless (but clearer to many than being too careful):
,A vertical asymptote occurs at #a# if #a# is a finite value for #x# that makes #y# become #oo# or #-oo#.

When we ask about the limit at infinity, we are asking if there is a finite values #b# that #y# approaches as x becomes #oo# or #-oo#.

The roles of #x# and #y# are reversed. Which one are we 'trying to make infinite'?

Be careful to distinguish the phrases "infinite limit" (#yrarr+-oo#)
as opposed to "limit at infinity (#xrarr+-oo#).

Here are 2 links. (I haven't yet learned to embed them nicely.)

Infinite Limits and Vertical Asymptotes: http://socratic.org/calculus/limits/infinite-limits-and-vertical-asymptotes

Limits at Infinity and Horizontal Asymptotes:
http://socratic.org/calculus/limits/limits-at-infinity-and-horizontal-asymptotes

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