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Unformatted text preview: MAC 2311 April 5, 2007 Exam III and Key Prof. S. Hudson. 1) (10pts) A spherical balloon is inflated so that its volume ( V = 4 r 3 / 3) is increasing at a rate of 3 ft 3 /min. How fast is the diameter increasing when the radius is 1 ft.? 2) (10pts) Compute each limit (and show work); a) lim x + (1- 2 /x ) x b) lim x tan( x ) tan- 1 ( x ) 3) (25pts) Compute: a) Find dy/dx : y = e 1 /x b) Find dy/dx : y = tan- 1 ( x 3 ) c) Find dy/dx using logarithmic differentiation: y = x x d) Find dy/dx using implicit differentiation: x 2 + y 2 = 100 e) Find d 2 y/dx 2 using implicit differentiation: 2 x 2- 3 y 2 = 4 4) (15 pts) Give an example of a function f ( x ) for each part, or explain why none exists. [Give three separate answers]. a) It has a stationary point at x = 0, but that point is not a relative extrema. b) It has a relative extrema at x = 0, but that point is not a stationary point....
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