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Unformatted text preview: NAME T.A. MATH 242, Fall 2007 Exam 2: October 31 Arrange your work as clearly and neatly as possible, and cross out incorrect work. Unless otherwise noted, you must justify all answers to receive full credit. You may not use calculators, notes, or any other kinds of aids. 1. (10 points) Identify and sketch the curve x2 + 4 x − 5 + 9 y2 = 0, labeling all vertices. d 1 sin−1 x = √ , 1 − sin 2 θ = cos2 θ, sin2 θ = 1 (1 − cos 2θ) 2 dx 1 − x2 1 d tan−1 x = , 1 + tan 2 θ = sec2 θ, cos2 θ = 1 (1 + cos 2θ) 2 dx 1 + x2 2. (12 points each) Evaluate each integral. (a) ln ( x + 1) dx (b) x3 4 − x2 dx 3. (12 points each) Evaluate each integral, or show divergence.
4 (a) 1 1 dx x3 − x ∞ (b) 1 xe− x dx 4. (15 points) Find equations for both lines tangent to the curve x = sin (2t), y = sin(t) at the origin. 5. (15 points) Carefully plot the polar curve r = 1 − sin θ, labeling at least four points. 6. (12 points) Find the area of the shaded region. r = 2 sin(θ) r=1 ...
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This note was uploaded on 04/03/2009 for the course MATH 242 taught by Professor Wang during the Fall '08 term at University of Delaware.
 Fall '08
 wang
 Math, Calculus

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