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Limits: Evaluation Techniques

Learn how to find limits using techniques such as multiplying by LCD, canceling out terms, substitution, and solving. Understand the concept of piecewise definitions for absolute value functions and how to rewrite fractions using LCD. Discover methods like rationalizing numerators, simplifying terms, and applying trigonometric limits. Explore examples and theorems, including the Property of Limits and the Squeeze Theorem, for effective limit evaluation.

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Limits: Evaluation Techniques

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  1. Limits: Evaluation Techniques 2.3

  2. Find the Limit -1 Multiply by LCD Cancel (4) Substitute and Solve

  3. Example -1 Multiply by LCD Cancel (2) Substitute and Solve

  4. Use piecewise definition for absolute value functions Limit DNE!

  5. Use piecewise definition for absolute value functions Limit DNE!

  6. Examples Cancel Substitute and Solve 64 16

  7. Rewrite as a single fraction using LCD D.S -> 0/0 Rationalize Numerator -1 Simplify Cancel 0 0 Substitute and solve

  8. TRIG LIMITS

  9. =1 Must match exactly!

  10. =0 Must match exactly

  11. EXAMPLES

  12. Multiply numerator and denominator by 3 Since they match…let’s use our theorem Property of Limits

  13. Trapped between: This makes a limit sandwich! 0 0 By Squeeze Theorem

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