131f10x2ForReview

131f10x2ForReview - d dx ( e 3 x tan x ) = 4. (12%)...

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Name (Last, First) ID # Signature Lecturer Section (A, B, C, etc.) university of massachusetts amherst department of mathematics and statistics Math 131 Exam 2 October 28, 2010 7:00-8:30 p.m. Turn of all cell phones and watch alarms! Put away iPods, etc. When calculating derivatives in #1–5, do not “simplify” your answers. But do use enough parentheses to show clearly how expressions are grouped together. For example, do not write x + 2 · x - 1 if you really mean ( x + 2)( x - 1). Do not use a calculator. Do all work in this exam booklet. You may continue work to the backs of pages and the blank page at the end, but if you do so indicate where. Organize your work in an unambiguous order. Show all necessary steps. Answers given without supporting work may receive 0 credit! Be ready to show your UMass ID card when you hand in your exam booklet. QUESTION PER CENT SCORE 1 12 2 12 3 12 4 12 5 12 6 12 7 12 8 12 Free 4 4 TOTAL 100
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1. (12%) Calculate: d dx ( 6 x - x 9 - 2 π ) = 2. (12%) Calculate: d dx p 2 x - 3 r x P 131 = 3. (12%) Calculate:
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Unformatted text preview: d dx ( e 3 x tan x ) = 4. (12%) Calculate: d dx sin ( ln(4 x + 28) ) = 5. (12%) Calculate: d dx p arcsin x x 5 + 25 P = 6. (12%) A particle is moving along the x-axis. At arbitrary time t , its position x ( t ) is given by: x ( t ) = t 3-9 t 2 + 15 t. (a) Find the particles velocity function v ( t ). (b) At what time or times, if any, is the particle at rest? (c) At what time or times, if any, does the particle have positive acceleration? 7. (12%) The graph of the equation e y cos x = sin( x y ) is shown below. Find the exact slope of the tangent line to this graph at its point ( / 2 , 0). 1 2 3 x 1 2 y 8. (12%) Let a be a positive constant (but a does not need to be an integer). Derive the formula for d dx ( x a ). Suggested way to start: Let y = x a . Take the natural log of both sides of that: ln( y ) = (simplify the right-hand side here) Now use implicit dierentiation. 1...
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131f10x2ForReview - d dx ( e 3 x tan x ) = 4. (12%)...

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