Math242E207

# Math242E207 - NAME T.A MATH 242 Fall 2007 Exam 2 October 31...

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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 x 2 + 4 x - 5 + 9 y 2 = 0, labeling all vertices. d dx parenleftBig sin - 1 x parenrightBig = 1 1 - x 2 , 1 - sin 2 θ = cos 2 θ , sin 2 θ = 1 2 ( 1 - cos 2 θ ) d dx parenleftBig tan - 1 x parenrightBig = 1 1 + x 2 , 1 + tan 2 θ = sec 2 θ , cos 2 θ = 1 2 ( 1 + cos 2 θ )

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2. (12 points each) Evaluate each integral. (a) integraldisplay

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