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Unformatted text preview: MAT286 Final Exam Fall 2004 1. Suppose that the slope of the tangent line to a function f ( x ) at any x is given by f ( x ) = 2 x 2 4 x + 3 . If the graph y = f ( x ) goes through the point (1 , 10), find the function f ( x ). 1 2 2. Consider the following function f ( x ) on the interval [0 , 2]: f ( x ) = x 2 + cos x + 4 . a) Find the exact area bounded by the curve and the xaxis on the given interval. ( Show all steps including the appropriate antiderivative and the evaluations. No credit will be given for providing only the final numerical value. ) b) Find the average value of the function f ( x ) on the given interval. 3 c) Set up, but do not evaluate the integral that gives the volume of the solid formed by revolving the region bounded by the curve y = x 2 + cos x + 4 and the xaxis on the given interval about the xaxis. d) Use your TI83 to evaluate the integral in part c). Round to two decimal places. 4 3. Find the following antiderivatives. Circle your answers....
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This note was uploaded on 06/17/2011 for the course MATH 286 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.
 Spring '11
 NA
 Slope

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