Chapter 5_sec2.pdf - Limits and Their Properties 1.3...

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Limits and Their Properties
Evaluating Limits Analytically 1.3
3 Evaluate a limit using properties of limits. Develop and use a strategy for finding limits. Evaluate a limit using the dividing out technique. Evaluate a limit using the rationalizing technique. Evaluate a limit using the Squeeze Theorem. Objectives
4 Properties of Limits
5 The limit of f ( x ) as x approaches c does not depend on the value of f at x = c . It may happen, however, that the limit is precisely f ( c ). In such cases, the limit can be evaluated by direct substitution . That is, Such well-behaved functions are continuous at c . Properties of Limits
6 Properties of Limits
7 Example 1 Evaluating Basic Limits
8 Properties of Limits
9 Example 2 The Limit of a Polynomial Solution :
10 The limit (as x 2 ) of the polynomial function p ( x ) = 4 x 2 + 3 is simply the value of p at x = 2. This direct substitution property is valid for all polynomial and rational functions with nonzero denominators. Properties of Limits
11 Properties of Limits
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