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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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**8-7 Indeterminate Forms & L’Hôpital’s RuleObjective:**Recognize limits that produce indeterminate forms, apply L’Hôpital’sRule Miss Battaglia AP Calculus**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**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 (-∞)/(-∞)**Indeterminate Form 0/0**Evaluate**Indeterminate Form ∞/∞**Evaluate**Indeterminate Form 0∞**Evaluate**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**Indeterminate Form 00**Evaluate**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.**Homework**• Read 8.7 Page 576 #11-39 odd, 81, 82

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