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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20A Midterm Exam 2. November 15, 2007 Turn off and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. 1. (3 points) Use logarithmic differentiation to compute the derivative of f ( x ) = cos(3 x )( x 3 + 1) e 3 x 3 x . Solution. We have ln f ( x ) = ln cos(3 x ) + ln( x 3 + 1) + 3 x- 1 2 ln(3 x ) . Differentiating (using the chain rule) we get f ( x ) f ( x ) =- 3 sin(3 x ) cos(3 x ) + 3 x 2 x 3 + 1 + 3- 1 2 x whence f ( x ) = parenleftbigg- tan(3 x ) + 3 x 2 x 3 + 1 + 3- 1 2 x parenrightbigg cos(3 x )( x 3 + 1) e 3 x 3 x ....
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- Fall '08