Unformatted text preview: Name Teaching Assistant Math 1502J 2pm Andrew 5 February 2004 Hour Test 1 Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but 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) Solve the initial value problem dy = y 2 sin(t ) . dt y (0) = 1
2. (25) Determine the convergence/divergence of these improper integrals. Determine the value of any convergent integral.
• • x † a. Úxe
0 dx b. Ú 1+ x
0 x 2 dx
1 Âk 2 ( x  4 )
k k=1 • 3. (25) a. Compute the radius of convergence of the power series † † k . b. Does the series in part a converge for x = 2, x = 5, x = 6, x = 7 ? Note that part b does not really depend on part a. † 4. (25) a. Calculate the Taylor polynomial P2 ( x ) , centered at 0, for the function † 1 f ( x) = ( 1 + x ) 2 . b. Estimate the accuracy with† which P2 (1.1) (i.e., x = .1) approximates 1.1 . You will not receive credit for simply comparing the value of P2 (1.1) with a value of 1.1 obtained by calculator.
† † † † † Name Teaching Assistant Answers: 1. y =
1 cos(t ) Page 2 of 2 Hour Test 1 5 February 2004 2. a. Converges to 1.
† b. Diverges 3. a. R = 2 b. Concerges at 5 and 2. Diverges at 7 and 6. 4. a. P2 ( x ) = 1 + 1 12 xx 2 8 b. .0000625 † ...
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 Spring '08
 Morley
 Calculus, Taylor Series, Convergence, Teaching assistant

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