INFINITE LIMITS

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INFINITE LIMITS

• Section 1.5

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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

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DEFINITION OF INFINITE LIMITS
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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

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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

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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

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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

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Evaluate

• infinity
• 0
• Negative infinity
• Does not exist

9
Evaluate

• infinity
• 0
• Negative infinity
• Does not exist