Limits of indeterminate forms 0/0

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Limits of indeterminate forms 0/0

• If an attempting to plug in the number when
  taking a limit yields 0/0, you arent done.
  Think of the problem as being broken and needing
  to be fixed.
• The following examples show some of the tricks
  for fixing broken limits.

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Factor and Reduce
The most basic broken limit is one that can be
factored and reduced. You create a function that
agrees at all but one point when you do
this. This is a removable discontinuity. The
original function has a hole at (5, 1/10).
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Look at the graph and table for the functions
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Rationalize the Numerator
If the numerator of an indeterminate form
involves radicals, try rationalizing the
numerator. You multiply by the conjugate (same
terms but the opposite sign between the 2
terms) Simplify and reduce.
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Examine the graph and table
The functions agree at all but one point.
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Complex Fractions
If you have a complicated fraction, the best
thing to do is simplify it. Review of
simplifying fractions.

• Get common denominators for the top and bottom.
• Flip the bottom
• Simplify
• Evaluate your limit

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Looking at the graph and table