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Solutions-166E2-S06

# Solutions-166E2-S06 - MA 166 Exam 2 Spring 2006 Page 1/4...

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Unformatted text preview: MA 166 Exam 2 Spring 2006 . Page 1/4 NAME MM 10—DIGIT PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4. . The test has four (4) pages, including this one. . Write your answers in the boxes provided. You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. . Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this test. Poem U! Find the integrals in roblems 1—5. I .. . (8) 1. / sec4xda: : ‘ segfx (\$94256 (fat) 0 '0 I . GD :f (”Mom (ms? “t: +ij w Md»! “NM—-44..“ 0 Wm- . aﬂ)“ ) " 2 'nziuefc (HM N“ ..... MA 166 f Exam ‘2 Spring 2006 Name —— Page 2/4 dt , 10 3. /—— Hint: l1n secm+tanm =seczz: A; ‘ ) t2—2t+5 ( dw ' ' Rm; ' GD f ”U 9 d W —- “WWW Z _7 .... 231189 Ma’m’g + 4 .Zfseag a9 dB (44:24am?! cltzzxqecd’zﬁdgﬁ 3&9???) :' ,lmtiim;+ ‘f/‘(V‘C’ (10) 4 / d1: (Epic; 'iqﬂswm IS. left mievwsyﬂ)t [:6] \$(1+\/_) (Hint: First make a substitution to express the integrand as a rational function) ﬁzfui21+:)q ( X—M dx::uzfu) ) MA 166 . 1 Exam 2 Spring 2006 Name _— Page 3/4 (9) 6. Determine the constants in the partial fraction expansion 5x2—\$+3 A\$+B C ___.____2_: 2 +— \$(1+\$) a: +1 17 leox-kﬁ :z 64x+5)7( + C (YEN) (,4+c)x1+ BX-t C (16) 7. Determine Whether each integral is convergent or divergent. Find its value if it is convergent. Important: You must show clearly how limits are involved. 1 —t X 30/ (—w2+2>2d ””@ gigolo (War h :L': ft:2T du a: X172, d“:2x4{y) H Sin-4t 3 II '51' A - 4° 9 (7) 8. Set up but do not- luate an integral for the length of the curve 31- — cos £L', 0 < a: < 27r xi, Wwiuf‘ W?M mount ’ \ \$ 'L =\/ 1+ (*ng w . 1*?“ W ‘ I u «6'! “ff/m ans-n WWW“ 1n. mama ma 2',er ‘”‘" 1+ ﬁzz/“ﬂat dx "(£441 ‘15,!“ 1 MA 166 ‘ ~ ' Exam2 Spring 2006 Name —' Page 4/4 (12) 9. Consider the lamina in the ﬁrst quadrant bounded by the curves y = 1 — 3:2, 31‘: 0 and y—— - 0, and with density p— - 1. Find the following: (a) )The mass m of the lamina ’2 1 _ 1““ 2 1 1 [ix m :fa—«UAX =L “EX-Jo WW)" 0 _ 1 _2 W2 2 ' '1'? -: 0 23-” y... (d) The center (If) mass (53,31) of the lamina .. 3 X 2 “Mi 1' —— M 8 a. My: A 2 (10) 10. Determine whether the sequence converges or diverges. If it converges, ﬁnd the limit (You need not show work for Ellis problem.) N PC . _ 77: + 1 I + 9‘1 a. (a) a" ‘ 3n — 1 3 W272 22-22222 32 M we ()0 ,L; D 3 2 7:; » :2 ”77 .L "L .L M-hwﬁm ‘2 {2"} £22 €32“) , 22224222 _ [email protected] (e) anznsin (l) n /- I ,5“; X 51%;): :1 mm: “TH/é»: WW) :5") ’ K, (C) {M} éh'flﬂ. ll (271w)! ’12”??? (2 "1’ W222“ Mb, 0 -€§; ( .220»: .1, 26-22% w =| .LEZJ X-atxs ' gawk: ...
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Solutions-166E2-S06 - MA 166 Exam 2 Spring 2006 Page 1/4...

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