8_7_Indeterminate_Forms_LHopitals

8_7_Indeterminate_Forms_LHopitals - 8.7 Indeterminate Forms...

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Unformatted text preview: 8.7 Indeterminate Forms and L'Hopital's Rule Study 8.7 p.574: 5 15, 19 25, 29, 37 45, 51 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: Homework (1 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Consider: ? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: Introduction (2 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule What about: p. 574 #2 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: Introduction (3 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule from Calc 1, Ch 3 Extended MVT: Given that both f(x), g(x) 1 continuous on [a,b], 2. differentiable on (a,b) and 3. g ' (x) 0 for any x on (a,b) Then there exists c on (a,b) such that f ' ( c) = f(b) f(a) g ' (c) g(b) g(a) Used to prove L'Hopital'sRule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: Extended MVT (4 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule L'Hopital's Rule Let f(x), g(x) be 1. differentiable on (a,b) containing c, except possibly at c itself. 2. g ' (x) 0 for any x on (a,b), except possibly at c itself. If : Then: provided the limit exists or is infinite. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: L'Hopitals Rule (5 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Indeterminate Forms: Determinate Forms: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: Indeterminate vs. Determinate Forms (6 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (7 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (8 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (9 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (10 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (11 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (12 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (13 of 16) 8.7 Indeterminate Forms and L'Hopital's Rule Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Par 2 Title: example (14 of 16) Title: Apr 307:20 PM (15 of 16) Title: Apr 307:33 PM (16 of 16) ...
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