Final, Fall '03, Questions

Final, Fall '03, Questions - Tufts iinivereiI.-_ir Math 12...

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Unformatted text preview: Tufts iinivereiI.-_ir Math 12 Department ef Mathematics; December 1?, BEIGE Final Exam Ne beeke, netee1 er ealenintere. Cress ent wth gmn tie net went 11.5 te grade. Yen HILLSI. give rensene Fer feii eredit. Yen are required te eign veer exam hunk. 1. [2D peints} Evaluate I 3, Tri’r . _ rice—m d /'m (in: _ {'1'} [in “It “fife-i 2m: 5': W Le: —;:.~~‘ i 3.; 1+3:E 2. [.I'Ji peiei‘e] Determine whether each ef the felitiWinp; series: is rerlvergern. er' divergent. Justify veer enewer hv eiting the appropriate eenvergenee teete. I II; 1 3'3 [_l]rI311 (a) 2‘ in.” + '3'“ -|. ] [m 2 FE}; - 'Fl=':| 1;..] 3. [T peinte] Find the retiiee nnti intervai el' ersmvergeeer: fer the Felireving newer enriee: Z i"i.i"ifl-' 3i" H n=i 1 '3':- ri- {T eeintej Given - T 1:” fer 33:1 e: 1.. find a. pewer eeriee repreeentetien fer — H"- -| nnf'l lief] — 4.1:], end etnte the refiine ef eenvergenee. 5. {12 peintej Let :rfit} = Zeinf end Mr} = -3eeet fer U E i f; it. fin} Find an equetien fer the underlying eerve by eliminating the parameter t. 1:th Siteteh n graph ef the parinnetrir: curve. Be sure te indicate the directien ef increasing t. (e) "Write an exnreeeien fer the iength ef the nerve here t = fl re t 2 tr, but DO NOT EVALUATE. Em EDN'IlNFJES ee REE'ERSE. I5. {d points] GGI'LKFIELEt the following pnints given in Cartesian coordinates to polar mur- dinates. (a) (—1—?) (h) E 1., J5) T. {1-1 puianl] [a] Shad} 1.113 polar Curve r T '2 2311119. [11] Find Hm nrna insidn the paint tum: r = 2 — 25in I9. 5. [8 pUthL-i} Find all uumplex TULJI'LIJ MIME nf .-. — —1E.'r. He 5mm Ln write ynur anawnrs in the farm :1 :-- bi. Pint the mats; in that mm;me plume. H. (H Imi'nts} L—Jnmputn and writn the following in standard E'urm1 u. —— bi. Z—i h . 'I _II' myflimi [up if}. {8 130111135} ‘Writt: expresaiunfi fur Lin: 113111111115 generated by rewirlvlufi L119. reginn hnu‘nd lag,» y - sin 3?, y — U, :r. = H, .1: = m-mmd the fellowng fines, bu: DD EVALUATE. h}w=-E {b} -::: —- 3 END '31-" EXEC-i ...
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Final, Fall '03, Questions - Tufts iinivereiI.-_ir Math 12...

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