# s10fe - x x f − = 2 a Find the interval(s on which f is...

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92-131 Final Exam Spring 2010 Name___________________ Brent Sect. 203 Determine the derivative of the following functions: 1) (5 pts) ) csc( ) ( 3 x x s = 2) (5 pts) 2 1 tan ) ( x e x f = 3) ) ( cos ) sin( x x y π = (10 pts) 4) 1 1 ) ( 3 2 + = t t t g (10 pts) 5) (5 pts) ) 1 ln 5 ( 5 + = x x y 6) (5 pts) ( 10 2 4 2 ) ( + + = x x x g ) 7) Using the limit definition of the derivative, calculate x d f d for . (10 pts) x x x f 4 3 ) ( 2 + = 8) Compute the derivative of the function (10 pts) t t t g )] [sin( ) ( = 9) Suppose a ball is moving on a linear track so that its acceleration (in m/s 2 ) is given by: 2 6 4 ) ( t t a = , for , 0 t where t is time in seconds. The ball has initial position 0 ) 0 ( = s m, and initially at rest. a ) What is the ball’s velocity after 3 seconds? b) When does it reverse direction? c) What is the ball’s position at any time t ? (10 pts) ) ( t s 10) Let x e
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Unformatted text preview: x x f − = 2 ) ( . a) Find the interval(s) on which f is increasing or decreasing. b) Find local (relative) maximum and minimum values of f . c) Determine intervals where the function is concave up and concave down. d) Are there any asymptotes? (10 pts) 11) Find the dimensions of the cylinder of largest volume that can be inscribed in a sphere of radius 1 ft (10 pts) 12) There is one positive value of x that solves the equation . 2 2 = − x a) Write down the recursion equation for solving this problem using Newton’s method. b) Starting with , use Newton’s Method to approximate the solution by . (Round to ) (10 pts) 2 = x 2 x 6 10 −...
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