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Spring05_M126 - jprmj ZDéS Mufti I16 Flh‘il 1 The lines...

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Unformatted text preview: jprmj ZDéS- Mufti I16 Flh‘il 1. The lines a: = 0, :3 ~—- 1, y = 0 and the curve y = $633 bound a region of the mgr—plane. If we rotate this region about the x—axis, what is the volume of the resulting solid? 2. (a) Find the Taylor series expansion of the function f =2 2:3 costs?) about 0. (b) Evaluate if WEIR—l)?” Use the series in part (a) to approximate f (l / 2) to within 1043. 3. Find the following indefinite integrals. I on f 133113 3: dm (a) [wk—5:? d2: 4. Find the area of the surface obtained by rotating the curve y 2' Qfi, 0 g a: S 8, about the r—axis. ' 5. Decide whether the following infinite series are absolutely convergent, ' conditionally convergent, or divergent. ' ‘ ' 1 oo (3’) gnlnn (b) EEan mam.ng "- 6. Sketch the curve given by the polar equation 7" = 4 — 25in 9. Find the area enclosed by the curve, 7. Determine whether the foilowing integrals are convergent or divergent. oo air/'2 (a) famgmdzc (b) {tenicdiv - 7r/2 8. Find 11m (mln(ac + 2) — mines). (Ev—FOO 9. Does the sequence on = (4)" - 5% converge as n m+ 00? If it does, find its limit. 10. Determine the radius of converge and the interval of convergence of the 2" (z—S)” 00 power series 2 3H1 71:0 ...
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