F09fe - f c Determine intervals where the function is concave up and concave down d Determine any points of inflection e Are there any asymptotes

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92-131 Final Exam (Brent Sec. 203 & 207) Fall 2009 Determine the derivative of the following functions: 1) ) ( tan ) ( x e x f = 2) ) arcsin( ) ( 3 x x s = 3) ) 3 ( sin 4 x e y x = 4) 1 1 ) ( 2 3 + = t t t g 5) 3 1 ln 3 x x y + = 6) ] [ ln ) ( 2 x x f = 7) Using the limit definition of the derivative, calculate x d f d for 1 ) ( 3 + = x x f . 8) Suppose that 0 1 2 2 = y e y x . Find x d y d , then find the equation of the line tangent to the graph of this equation at the point ) 1 , 1 ( . Write your answer in slope-intercept form. 9) Suppose a ball is moving on a linear track so that its acceleration (in m/s 2 ) is given by: 2 3 16 ) ( t t a = , for 0 t , where t is time in seconds. The ball has initial position s = 2 m, and initial velocity v = 0 m/s. a )What is the ball’s velocity after 3 seconds? b) When does it reverse direction? c ) What is the ball’s position ) ( t s ? 10) Let 2 / 2 ) ( x e x f = . a) Find the interval(s) on which f is increasing or decreasing. b) Find local (relative) maximum and minimum values of
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Unformatted text preview: f . c) Determine intervals where the function is concave up and concave down. d) Determine any points of inflection. e) Are there any asymptotes? 11) A storage bin with a ceiling and floor is to be constructed in the shape of a cylinder. The cost of the material used for the two circular surfaces is $10 per square foot. The material used for the lateral surface costs $20 per square foot. What are the dimensions of the cheapest bin that can be built with a volume of π 000 , 1 ft 3 ? 12) There is one positive value of x that solves the equation 3 3 = − x x . a) Give a recursion equation for solving this problem using Newton’s method. b) Starting with 2 3 = x , approximate the solution by 2 x ....
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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