ptest1 - PRACTICE TEST 1 FOR MATH1502KB (1) Compute the...

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Unformatted text preview: PRACTICE TEST 1 FOR MATH1502KB (1) Compute the following indefinite integrals (a) (b) (2) Compute the following improper integrals x3 + 1 dx, x2 + 3 1 dx, 2-x+2 x e-|x| dx, - (a) (b) 1 dx, + e-x - e dx (c) 1 x ln x (3) Are the following integrals convergent? Justify! 1 (a) dx, 2 sin x + x cos x (b) dx. 2 0 1+x (4) Compute the Taylor expansion of degree 5 of the following functions at x = 0. ex (a) cos x, (b) 1 + x2 , (c) e- 2 . (5) Solve the following equations with initial conditions dy (a) = e x , y(0) = 10; dx dy = y(y - 5), y(0) = 1; (b) dx dy (c) = e-x (1 + y), y(0) = 2. dx x2 1 ...
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