1065 - Math 202 Part I Final Exam Spring,2008 Do all parts...

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Math 202 Final Exam Spring,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 = 2 arctan(3 x ) ; (b) y = x 2 + x x ; (c) y = ln( q x 4 + 3 x ) . (2) Compute each of the following integrals(24 points): (a) Z x 3 p 4 + x 2 dx ; (b) Z x 3 - 1 x 3 + x dx (c) Z cos 3 ( x ) dx ; (d) Z 1 0 x ln( x + 1) dx. (3) Compute each of the following limits (10 points): (a) Lim x →∞ x 2 + e x x 3 + e x ; (b) Lim x →∞ x 1 /x . (4) The region R in first quadrant of the xy plane is bounded by the curves y = 9 - x 2 , y = 0 and x = 0. Set up two integrals (method of washers and method of shells) for the volume of the solid obtained by rotating R around the line x = 10. Do not compute the value of the integrals(10 points) (5) Sketch the curve given by the equation r = 2+cos( θ ) in polar coordinates, labeling the x and y intercepts, and compute the area it encloses. (8 points) 1
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1065 - Math 202 Part I Final Exam Spring,2008 Do all parts...

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