8_7_Indeterminate_Forms_LHopitals

# 8_7_Indeterminate_Forms_LHopitals - 8.7 Indeterminate Forms...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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) ...
View Full Document

## This note was uploaded on 09/09/2011 for the course MATH 1431 taught by Professor Any during the Fall '08 term at University of Houston.

Ask a homework question - tutors are online