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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 particle’s 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 ( π/ 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 di±erentiation. 1...
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- Fall '08
- Statistics, dx, Department of Mathematics, exam booklet, University of Massachusetts Amherst, UMass ID card