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Some limits can be found by direct substitution, while others cannot. The “Rules for Limits” exist to help in determining which limits can be found by substitution.
Rules for Limits
For any constants a and c, and any positive integer n...
if n is even, then c > 0
Summary of Rules for Limit Substitution
For functions composed of additions, subtractions, multiplications, divisions, powers, and roots, limits may be evaluated by direct substitution, provided that the resulting expression is defined.
Ex A: Find each limit by direct substitution.
Sometimes direct substitution into a quotient gives an undefined expression. If this happens, factoring, simplifying, and then using direct substitution may help.
Ex B: Find the limits by simplifying and then graph the function.
assignment
Part A: Find each limit by substitution. You may have to simplify first.
1.2 Notes & Homework
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1.2 Key
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