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2034 - Math 202 Part I Final Exam Fall,2008 Do all parts of...

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Math 202 Final Exam Fall,2008 Part I Do all parts of the following six problems. (1) Compute the derivative dy dx for each of the following (18 points) : (a) y = ln( 1 x + 1 ) . (b) y = arcsin( x ); (c) y = sin( x ) x + sin( x ); (2) Compute each of the following integrals(24 points): (a) Z x 3 + 2 x 3 - x dx ; (b) Z tan( x ) sec 4 ( x ) dx ; (c) Z p 4 - x 2 dx ; (d) Z 1 0 arctan( x ) dx. (3) Compute each of the following limits (10 points): (a) Lim x →∞ x e - x ; (b) Lim x 1 + x 1 / ( x - 1) . (4) The region R in first quadrant of the xy plane is bounded by the curves y = sin( πx ) and y = 2 x . Set up two integrals (method of washers and method of shells) for the volume of the solid obtained by rotating R around the line y = 2. Do not compute the value of the integrals(10 points) (5) Sketch the curve given by the equation r = 3+sin( θ ) in polar coordinates, labeling the x and y intercepts, and compute the area it encloses. (8 points) 1

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Part II Do all parts of three out of the following four problems (10 points each) (7) (a) A 16 pound pull extends a spring 6 inches (= one half of a foot). Compute the work done stretching the spring an additional foot. (b) Evaluate the integral or show it is divergent:
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