test110a

test110a - f described above b Estimate the accuracy with...

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Name 11 February 2010 Teaching Assistant Hour Test 1 Math 1502 J Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but are by no means necessary. Pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) a. Solve the initial value problem 7 ) 0 ( 2 3 = = - y e y dx dy x b. Find the general solution of the differential equation 2 2 y x dx dy = 2. (25) a. Evaluate the limit ) cos( 1 ) sin( lim 0 x x x x - . b. Determine whether the integral converges, and if so, evaluate the integral. - 0 2 dx e x x

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Name Page 2 of 3 Math 1502J Andrew Hour Test 1 Teaching Assistant 11 February 2010 3. (25) A mysterious function named f has these properties A. Whenever k is odd, the k-th derivative at 0 is ( 29 ( 29 0 0 = k f . B. ( 29 ( 29 ( 29 6 ) 0 ( , 4 ) 0 ( , 2 ) 0 ( ' ' , 1 0 6 4 - = = - = = f f f f C. ( 29 ( 29 8 8 x f for all x , 2 1 2 1 - x . a. Find the 7-th Taylor polynomial at 0 for the function
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Unformatted text preview: f described above. b. Estimate the accuracy with which this 7-th Taylor polynomial approximates -4 1 f . 4. (25) a. Determine which series converge and which diverge. Be sure to tell which convergence test you are using. i. ∑ ∞ = + 1 ! 5 1 k k k k ii. ∑ ∞ =-1 ) sin( 3 k k k iii. ∑ ∞ = +-1 ) ln( ) 1 ( ) 1 ( k k k k b. Calculate the radius of convergence of ( 29 ∑ ∞ = +--1 1 8 3 2 ) 1 ( k k k k k x k Name Page 3 of 3 Math 1502J Andrew Hour Test 1 Teaching Assistant 11 February 2010 ANSWERS 1. a. x x e e y 2 3 6 + = b. C x y +-= 3 3 1 1 2. a. 2 b. Converges to 2 1 3. a. ( 29 6 4 2 7 ! 5 1 ! 3 1 1 x x x x P-+-= b. ( 29 ( 29 ! 7 4 1 8 4. a. i. Converges by the Ratio Test ii. Diverges by the basic comparison test, compare to ∑ k 1 iii. Converges by the Alternating Series Test b. 2 3 = R...
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This note was uploaded on 09/07/2010 for the course CALC 1502 taught by Professor Morley during the Spring '08 term at Georgia Tech.

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test110a - f described above b Estimate the accuracy with...

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