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Miss Battaglia AP Calculus

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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

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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 (-∞)/(-∞)

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Evaluate

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Set the limit equal to y Take the log of both sides Tweak L’Hopital’s Rule Solve for y

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Evaluate

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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.

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

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