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Miss Battaglia AP Calculus

8-7 Indeterminate Forms & L’Hôpital’s Rule Objective: Recognize limits that produce indeterminate forms, apply L’Hôpital’s Rule. Miss Battaglia AP Calculus. The Extended Mean Value Theorem.

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Miss Battaglia AP Calculus

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  1. 8-7 Indeterminate Forms & L’Hôpital’s RuleObjective: Recognize limits that produce indeterminate forms, apply L’Hôpital’sRule Miss Battaglia AP Calculus

  2. The Extended Mean Value Theorem If f and g are differentiable on an open interval (a,b) and continuous on [a,b] such that g’(x)≠0 for any x in (a,b), then there exists a point c in (a,b) such that

  3. L’Hôpital’sRule Let f and g be functions that are differentiable on an open interval (a,b) containing c, except possibly at c itself. Assume that g’(x) ≠0 for all x in (a,b), except possibly at c itself. If the limit of f(x)/g(x) as x approaches c produces the indeterminate form 0/0, then Provided the limit on the right exists (or is infinite). This result also applies if the limit of f(x)/g(x) as x approaches c produces any one of the indeterminate forms ∞/∞, (-∞)/∞, ∞/(-∞), or (-∞)/(-∞)

  4. Indeterminate Form 0/0 Evaluate

  5. Indeterminate Form ∞/∞ Evaluate

  6. Applying L’Hôpital’sRule More Than Once Evaluate

  7. Indeterminate Form 0∞ Evaluate

  8. When substitution produces 1∞, 1-∞, 00, ∞0 • Set the limit equal to y • Take the log of both sides • Tweak • L’Hopital’s Rule • Solve for y

  9. Indeterminate Form 00 Evaluate

  10. Classwork Evaluate the limit using techniques from Chapter 1 & 3 then evaluate using L’Hopital’s Rule. 1. Evaluate using L’Hopital’s if necessary 2. 3. 4.

  11. Homework • Read 8.7 Page 576 #11-39 odd, 81, 82

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