M21exam4W99

# M21exam4W99 - 1. (8 pts) Use the Maclaurin series for e x...

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1. (8 pts) Use the Maclaurin series for e x to find a power series for xe x 3 2 - . _________________________ 2. (a) (8 pts) Find the 3rd degree Taylor polynomial Tx 3 (29 for fx x (29 = sin at a = π 6 . ___________________________________________________ (b) (4 pts) Use Taylor’s formula to estimate the accuracy of the approximation sin xTx ≈ (29 3 (from part (a)) when x [] 0 3 , π . _________________________

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3. (10 pts) Solve the initial-value problem ′ = y ye x 1 2 , y 01 (29 = . _________________________ 4. (10 pts) Set up, but DO NOT evaluate, a definite integral that gives the area of the surface obtained by rotating the curve yx =+ 2 1 , 49 ≤≤ x , about the x -axis. Be sure the integrand is expressed in terms of the variable of the integration. _________________________ 5. (12 pts) Find the centroid of the triangular region with vertices (0,0), (3,0), and (3,2). _________________________
6. (10 pts) A trough is filled with a liquid whose weight density is 62.5 lb/ft 3 . Each end of the trough is an equilateral triangle with sides 4 ft. long and vertex at the bottom.

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## This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.

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M21exam4W99 - 1. (8 pts) Use the Maclaurin series for e x...

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