MATH 142 Final: MATH142 South Carolina 03Final Exam3s
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For the fall 2012 term : compute the improper integral: z 0. 4 x2 + 1 (a) 1 + 2 (b) 0 (c) divergent (d)* 3. 3(cid:17)dx (e) 2 ln 3 (f) ln 4 + 3. 4: the area of the region bounded by y = cos(2 x), the x-axis, and the vertical lines x = 0 and x = 1. 4: the region of the xy-plane bounded by y = e x/2 and the x-axis for 0 x ln(2) is rotated about the x-axis. The volume of the resulting solid of revolution is: (a) 2 : the length of the arc of curve y = 1. [hint: eventually use the identity: a4 + 1. 4x for 1 x 2 is: (e) 1 (d) 2 (f) e2: the sequence xn = 1 3n5 n is: (a) divergent to (b) divergent to (c) unbounded (d)* convergent: the interval of convergence of the series. Then y(e (c) (d) 1 (e)
