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Section 5.2.3 Day 2 Limits Review

Section 5.2.3 Day 2 Limits Review. Lesson Objective: Students will: Understand the necessary conditions for a limit to exist. Practice finding limits. Predict limits from tables. ( 1). General Idea: Behavior of a function very near the point where

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Section 5.2.3 Day 2 Limits Review

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  1. Section 5.2.3 Day 2 Limits Review

  2. Lesson Objective: Students will: • Understand the necessary conditions for a limit to exist. • Practice finding limits. • Predict limits from tables.

  3. (1).General Idea: Behavior of a function very near the point where (2). Layman’s Description of Limit(Local Behavior) L If x approaches a, from both sides, then the function approaches a single number, L. a (3). Notation (4). Mantra

  4. 4 Ways to Depict Limits G N A W Graphically Numerically Analytically Words

  5. G N A W Graphically

  6. FINDING LIMITS • Graphically

  7. G N A W • Numerically • Words Mantra:

  8. FINDING LIMITS • Analytically Rem: Always start with Direct Substitution

  9. FINDING LIMITS • Analytically

  10. (1). If a is in the domain: Use Substitution

  11. (2). If a is not in the domain: Start with Substitution A. If the result is , ( this step must be shown), then factor and substitute again.

  12. Graphically Since the function is undefined at x = 3, this produces a “hole” in the graph.

  13. (2). If a is not in the domain: Start with Substitution B. If the result is , ( this step must be shown), then factor and substitute again.

  14. Graphically Since the function is undefined at x = 3, this produces a “hole” and an asymptote in the graph.

  15. Polynomials (Power Functions)

  16. Rational Functions

  17. Rational Functions Divide all terms in the numerator & denominator by the largest degree in the denominator.

  18. Rational Functions Divide all terms in the numerator & denominator by the largest degree in the denominator.

  19. Leading Term Test Take the ratio of the leading terms.

  20. Examples

  21. Examples

  22. Examples

  23. Assignment WS 13.1#7-32

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