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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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 Fall '07
 Mikulevicius
 5%, 0 g, $633

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