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Determining Limits From Equations

This guide explores the process of determining limits from mathematical equations, focusing on indeterminate forms. Utilizing properties outlined in the textbook, we delve into various methods for solving these limits, including factoring and canceling, expanding and simplifying, rationalizing the denominator, and finding a common denominator. With practical examples, we illustrate each method's application, including cases with removable discontinuities. This resource equips students with essential techniques for limit evaluation in calculus.

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Determining Limits From Equations

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  1. Determining Limits From Equations • The Limit Properties found on p.35 of the textbook can be used. • Examples: 1) Determine

  2. Indeterminate Limits • Example 1 : Find

  3. Methods of Finding Indeterminate Limits • Factor and Cancel • Expand and Simplify • Rationalize the Denominator • Get a Common Denominator

  4. Example 2: • Find

  5. Example 3 • Find

  6. Example 4 • Find

  7. Example 5 • Find

  8. …Example 5 continued • This function has a removable discontinuity. • To remove it, make

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