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e309pmk - MAC 2311 Exam III and Key PM April 3 2009 Prof S...

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MAC 2311 PM April 3, 2009 Exam III and Key Prof. S. Hudson 1) [20 pts] Ch 4.1-3, Compute the derivative, y y = log 2 (3 x 4 ) Use the f - 1 theorem to compute y when y = sin - 1( x ), and simplify. 2) [10 pts] Find the dimensions of the cylinder with maximal volume that can be inscribed in a cone with radius 6 and height 10. You may need to use similar triangles at some point (or maybe the y = mx + b formula instead). 3) [10pts] Find the relative extrema of f ( x ) = x 3 ( x + 1) 2 and classify (as max/min). 4) [10 pts] Give an example of each. For maximal credit, give formulas (or, pictures are OK for partial credit). a) A function with an absolute max which is not a relative max. b) A function with a critical point which is not a stationary point. 5) [20 pts] Compute the limits using L’Hopital’s Rule. a) lim x π sin( x ) x - π = b) lim x →∞ (1 + 3 /x ) x = 6) [20 pts] Answer True or False. You do not have to explain. Do not make unstated assumptions (that f is positive, continuous, etc).

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