Day37-1432class - Math 1432 Register for Test 3 Don’t...

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Unformatted text preview: Math 1432 Register for Test 3 Don’t forget online quizzes. THINK: Which word will carry on the sequence? Half-mast, Taverner, Riparian, Nobility, Yuletide, ? Doubloon Exciting Macaroni Overtone Sky Pilot Ticklish Section 11.5 Taylor Polynomials in x Taylor Series in x Section 11.6 Taylor Polynomials Taylor Series in x – a Definition of nth degree Taylor polynomial: If f has n derivatives at c, then the polynomial ( 29 ( 29 ( 29( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = +- +- + +- n 2 n n c c P x c c x c x c x c 2! n! f '' f f f ' . . . is called the nth degree Taylor polynomial for f at c. Popper Number 31 1. Give the 7 th degree Taylor polynomial approximation for f (x) = e x centered at x = 0. - +- +- + + + + + + + +- +-- +- 2 3 4 5 6 7 2 3 4 5 6 7 2 4 6 3 5 7 x x x x x x a. x 2 3 4 5 6 7 x x x x x x b. 1 x 2 3 4 5 6 7 x x x c. 1 2 4 6 x x x d x 3 5 7 ! ! ! ! ! ! ! ! ! . ! ! ! 2. Give the 7 th degree Taylor polynomial approximation for f (x) = sin (x) centered at x = 0. - +- +- + + + + + + + +- +-- +- 2 3 4 5 6 7 2 3 4 5 6 7 2 4 6 3 5 7 x x x x x x a. x 2 3 4 5 6 7 x x x x x x b. 1 x 2 3 4 5 6 7 x x x c. 1 2 4 6 x x x d x 3 5 7 ! ! ! ! ! ! ! ! ! . ! ! ! 3. Give the 7 th degree Taylor polynomial approximation for f (x) = cos (x) centered at x = 0. - +- +- + + + + + + + +- +-- +- 2 3 4 5 6 7 2 3 4 5 6 7 2 4 6 3 5 7 x x x x x x a. x 2 3 4 5 6 7 x x x x x x b. 1 x 2 3 4 5 6 7 x x x c. 1 2 4 6 x x x d x 3 5 7 ! ! ! ! ! ! ! ! ! . ! ! ! 4. Give the 7 th degree Taylor polynomial approximation for f (x) = ln (x+1) centered at x = 0. - +- +- + + + + + + + +- +-- +- 2 3 4 5 6 7 2 3 4 5 6 7 2 4 6 3 5 7 x x x x x x a. x 2 3 4 5 6 7 x x x x x x b. 1 x 2 3 4 5 6 7 x x x c. 1 2 4 6 x x x d x 3 5 7 ! ! ! ! ! !...
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This note was uploaded on 03/06/2011 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.

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Day37-1432class - Math 1432 Register for Test 3 Don’t...

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