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Unformatted text preview: MAC 2311 Feb 9, 2005 Exam II and key Prof. S. Hudson. 1) [10pts] Find the max and min values of f ( x ) = 5 12 x 9 x 2 on [1,1]. 2) [10pts] Find the max and min values of f ( x ) =  2 x 3  on [0,2]. 3) [10pts] Compute the derivative of y = x 2 x using logarithmic diff’n. 4) [10pts] Compute y given that cos( xy ) = y , using implicit differentiation. 5) [5pts each] Compute y using any valid method. a) y = 3 x 2 x +1 b) y = x 2 cos( x ) c) y = sin( x 3 ) d) y = x 7 tan( x ) e) y = ln(ln( x )) 6) (10 pt) Use a linear approximation to estimate cos(43 o ). 7) (15 pts) A man 6 ft tall walks with a speed of 6 ft/s away from a street light that is atop a 12foot pole. How fast is the tip of his shadow moving along the ground when he is 100 ft from the pole? 8) (10pts) CHOOSE ONE; (remember to explain properly) A) Use the definition of derivative (a limit) to show that the derivative of sin( x ) is cos( x )....
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 Spring '08
 STAFF
 Calculus, Derivative, Product Rule, 5 pts, 5pts, 10 pt, 6 ft

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