INFINITE LIMITS Section 1.5

When you are done with your homework, you should be able to… Determine infinite limits from the left and from the right Find and sketch the vertical asymptotes of the graph of a function

DEFINITION OF INFINITE LIMITS

DEFINITION OF VERTICAL ASYMPTOTE If approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line at is a vertical asymptote of the graph of

Yes, vertical asymptotes at No holes. No vertical asymptotes or holes. Does the graph of the following function have any vertical asymptotes or holes? Yes, vertical asymptotes at No holes. No vertical asymptotes or holes. Yes, a vertical asymptote at and a hole at

A THEOREM CONCERNING VERTICAL ASYMPTOTES Let f and g be continuous on an open interval containing c. If , , and there exists an open interval containing c such that for in the interval, then the graph of the function given by has a vertical asymptote at

Properties of Infinite Limits Let c and L be real numbers and let f and g be functions such that and Sum or difference Product Quotient Similar properties hold for one-sided limits and for functions for which the limit of f as x approaches c is

Evaluate infinity Negative infinity Does not exist

Evaluate infinity Negative infinity Does not exist