math20 midterm2 2000-pg1

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Your Name Section Number Your TA’s Name Section Time I agree to abide by the Honor Code. Signature Math 20 Winter 2000 Prof. Moore Midterm 2 Directions: You may use a graphing calculator to compute and graph things during the exam, but you may not use any notes or books, or receive help from any person. Show all of your work, explaining as much as possible. 1. Find each of the following: a) (7 points) 5 θ - 4 θ 3 + 2 cos θ b) (7 points) sec 2 y + y ( y - 3 + y - 3 / 2 ) dy

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1. c) (8 points) 1 0 (3 x + e x ) dx . Simplify your answer as much as possible for this part.
2. Determine whether each of the following statements is true or false, writing out the word “true” or “false” in your answer. If the statement is true, provide an appropriate justification. If the statement is false, provide a counterexample. a) (6 points) If f is not the constant function f ( x ) = 0 on the entire interval [ a, b ], then b a f ( x ) dx = 0. b) (6 points) If b a f ( x ) dx 0, then f ( x ) 0 on [ a, b ].

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2. c) (6 points) The function - x 3 3 cos x is not an antiderivative of x 2 sin x .
3. a)

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• Winter '02
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