1. Limits of indeterminate forms 0/0 If an attempting to plug in the number when taking a limit yields 0/0, you aren’t 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.

2. 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).

3. Look at the graph and table for the functions

4. 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.

5. Examine the graph and table The functions agree at all but one point.

6. Complex Fractions If you have a complicated fraction, the best thing to do is simplify it. Review of simplifying fractions. Review of simplifying fractions. Get common denominators for the top and bottom. Flip the bottom Simplify Evaluate your limit

7. Looking at the graph and table