MATH 132 Midterm: MATH 132 UMass Amherst math132_spring04_html spring03-t2
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Your section: no notes, no books, it is not su cient to simply write down the answers. Note: how you arrive at your answers: you have 90 minutes. sin2 = Consider the parametric curve given by x = t2. [10 points] (a) determine all points (x, y) at which the parametric curve has vertical tangent. [10 points] (b) determine the equation of the tangent line at the point (x, y) = (3, 6) of this parametric curve. [10 points] for each of the following integrals, determine whether it is convergent or divergent. 0 dx x ln x (b) [5 points] z /3. [10 points] determine the area of the region that lies inside r = 3 cos and outside r = 2 cos . For each of the following in nite series, determine whether or not it is convergent or not. For the ones that do converge, compute its sum.
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