Fall 2007 - Hohnhold's Class - Quiz 1 (Version B)

Fall 2007 - Hohnhold's Class - Quiz 1 (Version B) - Quiz 1...

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Quiz 1 for Math 20B. Fall Quarter 2007, UCSD Henning Hohnhold Name: Section: #1: #2: Total: (1) (3 points) Compute the derivative of the function g defined by g ( x ) = Z e x 1 t · sin( t 2 ) dt. Solution: Using the FTC, part 1, and the chain rule, we compute d dx Z e x 1 t · sin( t 2 ) dt = e x · sin(( e x ) 2 ) · e x = e 2 x · sin( e 2 x ) , where the second factor in the second expression from the left comes from the interior derivative: d dx e x = e x .
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(2) (7 points) Evaluate the following integrals: ( a ) Z x 2 · cos ± 3 x 4 ² dx and ( b ) Z 5 - 1 x 2 · x + 2 dx. Solution: (a) We use integration by parts with u = x 2 and v 0 = cos ( 3 x 4 ) : Z x 2 · cos ± 3 x 4 ² dx = x 2 · 4 3 · sin ± 3 x 4 ² - Z 1 2 · 4 3
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Fall 2007 - Hohnhold's Class - Quiz 1 (Version B) - Quiz 1...

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