271FE-F2002

271FE-F2002 - MA 271 FINAL EXAM FALL 2002 Name Determine...

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Unformatted text preview: MA 271 FINAL EXAM FALL 2002 Name Determine Whether the given series converge absolutely, converge conditionally, or diverge. Give reasons for your answers. 1. Z (—1)” tan‘1 n 00 —1"srnn 2 ;( 1>+n2u 3 Z<—1>“<W—¢fi> 0° _1nn3 4. 2:31—( 3)” 5. Find the interval of convergence of 00 (93 - 1)" gym + 1) 6. Find the Taylor polynomial of $6932 of order 7 at :1: = O. . . ' m3 (_1)nx2n+1 7. The apprOXImatlon sma: N a: — g +' ' '+ ——(2n + 1)! n needed to estimate sin(0.1) with an error of less than 10—10 is used. Determine the smallest 2 8. Compute limw. (6—)01 — cos(3$) 9. Find a series solution for y’ — y = x, 31(0) 2 O. 10. Find the arc length of the curve r(t) = (6‘ sint,et cost, et), 0 S t < 1. 11. Find an equation of the tangent plane to the surface :1: —— z = y2 at (1, 0, 1). 12. Classify the critical points of the function Hazy) = x3 - 3/3 — 3mg- . Find the maximum value of $33122 subjected to the constrain 311: + 23/ + z = 12. . Find the area of the image of the rectangle [0, 2] X [0,1] under the map T(u,v) = (U3 + 0,311). . Set up a triple integral for the volume of the solid bounded by the paraboloids z=2(x2+y2) andz= 12—x2—y2. . Let C be the curve given by r(t) = (t2,t3,t4), 0 g t g 1. Evaluate the line integral /(xy — zz)d$ + (yz —— m2)dy + (250 — y2)dz. 0 . Let C’ be the circle 1:2 + y2 = 4 oriented counterclockwise. Evaluate / y dz: — a: dy 0 $2 + 21/2 . . Let S' be the sphere x2 + y2 + z2 = 4 with outward normal and F 2 (any2 + z, y22 + :6, 2x2 + y). Compute F - nda. s . Let S be the portion of the cone 22 = m2 + y2 with 0 g z 3 2. Compute We . Let S be the portion of the paraboloid z = $2 + (If, 2 S 4 with downward normal and F = 3:2, yz, my). Compute < //S(V><F)-nda. ...
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271FE-F2002 - MA 271 FINAL EXAM FALL 2002 Name Determine...

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