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fin09k - MAC 2311 Final Exam AM Prof S Hudson 1(10 pts...

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MAC 2311 AM April 24, 2009 Final Exam Prof. S. Hudson 1) (10 pts) Compute y 0 ; a) y = (2 x ) x b) y = log 3 (2 x + 1) 2) (10 pts) Solve this Initial Value Problem: y 0 ( t ) = e t + t and y (0) = 2. 3) (25 pts) Compute and simplify; R e 2 x dx = R t 1+16 t 2 dt = R 1 - 2 t 3 t 3 dt = R cos 2 ( x ) dx = R tan 2 ( x ) dx = 4a) (10 pts) Find the slope of the tangent line to the curve, x = t , y = 2 t +1 at t = 1. For maximum credit, use the chain rule as done in class. 4b) (5 pts) For the same curve as above, find d 2 y/dx 2 when t = 1. 5) (10 pts) Sketch a graph of y = x 2 - 1 x 3 . Find all critical points, inflection points and asymptotes [and label them clearly]. You may use: y 0 = 3 - x 2 x 4 y 00 = 2( x 2 - 6) x 5 3 1 . 8 6 2 . 4 1 . 8 - 3 0 . 18 2 . 4 - 3 0 . 07 1
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6) (20 pts) Answer TRUE or FALSE: f ( x ) = ln | x | is an increasing function. A rational function is continuous except where the denominator is zero. The function cot( x ) is continuous on the interval ( - π/ 4 , π/ 4). If f is a polynomial, then it has exactly one antiderivative whose graph contains the origin.
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