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# final-1 - Name TA Math 20A Final Examination December 9...

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Name: PID: TA: Sec. No: Sec. Time: Math 20A. Final Examination December 9, 2008 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. # Points Score 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 9 9 6 Σ 57

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1. Find the following limits: (a) (2 points) lim x 0 3 x - 1 x (b) (2 points) lim x 0 + x log( x ), (c) (2 points) lim x 0 + x 3 x .
2. Compute the following integrals: (a) (3 points) integraldisplay 4 0 x dx (b) (3 points) integraldisplay 4 0 16 - x 2 dx (Hint: Use geometry and interpret as an area.)

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3. (6 points) Find the point(s) on the ellipse given by x 2 +3 y 2 = 1 where the tangent line has slope 1.
4. Let f ( x ) = radicalbigg x + 2 x - 2 .

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final-1 - Name TA Math 20A Final Examination December 9...

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