Calculus 3 Practice Exam 2

Calculus 3 Practice - a a × b b a × b c Bonus Find the radius and interval of convergence of ∞ X n =1 x-2 n n 2 Math 209 Exam 2 Practice 1 1

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Math 209 Exam 2 Practice 1. (13) Find a power series expansion (of at least four terms) for f ( x ) = e x - 1 x . 2. (13) Find a power series expansion (of at least four terms) for f ( x ) = cos ( x ). 3. (24) Given: x - sin x x 3 = 1 3! - x 2 5! + x 4 7! - x 6 9! + ··· a. Find at least four terms of the power series for Z x - sin x x 3 dx b. How many terms must be added to evaluate Z 1 0 x - sin x x 3 dx accurately to four decimal places ( | error | < 0 . 00005)? c. Evaluate Z 1 0 x - sin x x 3 dx accurately to four decimal places. 4. (13) Find the angle θ between the vectors a = < 3 , - 1 , 4 > and b = < - 5 , 2 , 1 > . 5. (12) Find accurately to the nearest tenth of a degree the direction angles θ x , θ y and θ z for the vector a = < 8 , - 1 , 4 > . 6. (13) Given a = < 1 , - 1 , 2 > and and b = < - 1 , 1 , 2 > , find Proj a b , the vector projection of b onto a . 7. (12) [Note: There was a mistake on this problem in the version I handed out in class, so use this version instead] Given a = < 2 , - 1 , 5 > and b = < 4 , 2 , - 1 > and c = < 3 , 1 , - 2 > , find
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Unformatted text preview: a. a × b b. a × b · c Bonus: Find the radius and interval of convergence of ∞ X n =1 ( x-2) n n 2 Math 209 Exam 2 Practice 1. 1 + x 2! + x 2 3! + x 3 4! + ··· 2. 1-x 2! + x 2 4!-x 3 6! + ··· 3. (a) x 3!-x 3 3(5!) + x 5 5(7!)-x 6 6(9!) + ··· (b) 1 3!-1 3(5!) + 1 5(7!)-1 6(9!) + ··· (c) Since —error— < 1 / 20 , 000 and 5(7!) = 25 , 200, two terms are sufficient for four decimal place accuracy. So the integral equals 1.9667. 4. θ = 117 . 7 ◦ 5. θ x = 27 . 3 ◦ , θ y = 96 . 4 ◦ and θ z = 63 . 6 ◦ . 6. Proj a b = ± 1 / 3 ,-1 / 3 , 2 / 3 ² 7. (a) ±-9 , 22 , 8 ² (b)-21 Bonus: R = 1, interval of convergence [1 , 3] . Page 2...
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This note was uploaded on 04/18/2008 for the course MATH 209 taught by Professor Bales during the Spring '08 term at Tuskegee.

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Calculus 3 Practice - a a × b b a × b c Bonus Find the radius and interval of convergence of ∞ X n =1 x-2 n n 2 Math 209 Exam 2 Practice 1 1

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