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test3-02 - Department of Mathematics University of Toronto...

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Department of Mathematics, University of Toronto Term Test 3 – March 13, 2002 MAT 137Y, Calculus! Time Alloted: 1 hour 50 minutes 1. Evaluate the following integrals. (6%) (i) e t 1 e t dt . (6%) (ii) sin 5 x cos 2 x dx . (7%) (iii) x 2 x 1 x 3 2 x 2 x dx . (7%) (iv) 3 1 1 dx x 2 2 x 2 2 . (7%) (v) 12 5 dx x x 4 . (7%) (vi) 1 0 x arctan x dx . 2. Evaluate the following expressions. (5%) (i) d dx arcsin x ln 1 e 2 x . (5%) (ii) d dx ln x x 2 . (5%) (iii) lim x 0 cos x cot 2 x . (15%) 3. Consider the area bounded by the curve y x x 2 and the x -axis. The line
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