Techniques for Computing Limits: The Limit Laws

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Evaluating Limits Analytically

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Presentation transcript:

Techniques for Computing Limits: The Limit Laws 1.6 Techniques for Computing Limits: The Limit Laws

Computing Limits Basic Limits: For real numbers b and c, and positive integers n:

Properties of Limits

Properties of Limits (continued)

Methods for Computing Limits A. “Plug-Ins” Using these basic limits and properties of limits, we can prove that the limit at c of the following kinds of functions can be evaluated by direct substitution of c for x: Polynomial Function Rational Function with c in its domain Radical Function with c in its domain Trigonometric Function with c in its domain

Examples

Methods for Computing Limits B. Rational Functions without c in their domain (“Single Holes”)

Example 4

C. Functions with Radicals

D. Special Trigonometric Limits Theorems:

Examples of use:

The Squeeze Theorem

Example using the Squeeze Theorem: (Watch Video) Proof of by the squeeze theorem:

Another example using the Squeeze Theorem: