Solutions-166E2-S01

# Solutions-166E2-S01 - MA 166 EXAM 2 Spring 2001 Page 1/4...

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Unformatted text preview: MA 166 EXAM 2 Spring 2001 Page 1/4 STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, student ID number, 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. 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. “>005? U! Evaluate the integrals in problems 1—5. (6) 1. /tan2:z:da: :: fﬁzczx €91) (1.x NC @ E1 {n+1 » No mufﬁn».an / \$3+\$d\$ ,i :V Xf'i «1: _;A_. +- E-xg—mé C‘CCcLit waﬁygmd x3+>< x (ﬁn) X 5‘ +1 190‘“? 4" C99 C73 Mfume; m X +L -: AXZ+A +BXZ+CX “womb Aura-:0 C:l. Azi (3;..L S le :1 + Ex +03“ :ﬁrmgi... +4.04), x2“. x W“ x2+1 :J/nlxl -—— éQmﬂxZ+L> +3tamui>< +vC ‘1 M fav- wash/00 +C (om. t£m€L «Ova»? £0?“ test) -1 {nor rwx'sm'vva Ax ’ dun) (our. ’Cim, <2ng ‘Lmv haggl‘ rmlolem) C73 @ @ lexl ~%h(><ai)+tarwix +C. i: MA 166 Exam 2 Spring 2001 Name ___________ Page 2/4 © <—- opt); for Fleim qua» Wrong V (12) 3- /:v3\/1+x2d:c : ftqnaeaecfew: m X: tome OLX:SCczedﬁ ' 441 ~x m N on Th. Suﬁsh‘tuimv; My :SCCG url-F‘x ‘ ' will 0:759 WorLL 2f townie Stanza:- metmew ,Lwr W [m6 m = {(\$9.36 ~1) 3.236 ametmaw _ zjtwmujz.) ( U» :: MCG’ de: Sicgtan6&9 ‘3 3 U LL? C secs 3 2......__. ': ~____s<zce S 3 + 5* ,5 +C :32. '1+x“5’/‘__g, 2.3/1 _ 3rd” (yummy?th 5( ) «5(L+X) +C m femeQQ: (a awed“. .150”th » awry”: .15 C (g @ (12) 4. /\/1—4\$2d:c :2: CJO\$29 dB , gqme qmﬁQng ruler 2.x ZX=9WG dung—026cm M ,w. [avobtem 3, 1_4X"L 1'4X1 =CQge’ (’L+ 003299433 : £86429) «PC 3% (9 +\$imems® +C ’- Lgtal‘ﬁthX) + Qx‘{1,-4>x""] +C : 4+" @ a BM}: 4 anw 1 wepenmm a a o N, .1. <5x‘n‘ 2x 14631th + w in unwed} ’ 4' ( )+ 2 } (6) 5. /:cos3acda: -_—_ _.\${Y11x)CJOSxoLx : convergent. Imgortant: Show clearly how limits are involved. 00 (a) /0 ate—32m: :: rtXEP'chleCa face 0 a 1— /. 1 3.19"" 3‘", 1,63 “‘4” [~:€‘*l=bm (“ﬁe * )-—~~«:~: o 1”” ? La. 3 1 . 3 7 '““ (b) dz: 1: m I ’l. AFC r—eo m _ 1 t —-> if t Xvi 0L“ ® g; p MA 166 Exam 2 Spring 2001 Name _____________ Page 3/4 (12) 6. Determine Whether each integral is convergent or divergent. Find its value if it is 72., , W g {1: =L‘m Wallis-755??? WW =°° T _ OLjumaAA/JCD (10) 7. Find the length ofthe curvey=%(m2+2)%,0§a:§l. :1. :2 \l (ll-9. ’2' ’ L. f0 +(Cbx) (ELM . '2, '2, ‘A 7’ L 2 we) +ew 2x>=4+><<w> : L )( x43? 2X1: LL%XZ)L L :— XLVO—Hzlz £le :: §1(l+><l)dh< G5) 0 a .. X3 ' l ’51-. “Xi‘g [Cpl-tirrgé) ﬁg— E) S (8) 8. Set up an integral for the area %of the surface obtained by rotating the curve 3; = Inst, 1 _<_ cc 3 2, about the cc-axis. Do not evaluate the integral. ~ A MA 166 Exam 2 Spring 2001 Name m Page 4/4 (12) 9. Consider the lamina bounded by the curves y = 332, y = 0, a: = 1, and with density p = 1. Find the following: (a) The mass m of the lamina. 4 11 1 _ 7, x i, :3. C29. “ﬁlm-tale 3 m k 4' (b) The moment My of the lamina about the y-axis. i 4» I 2. x,4r_...l— _L €53 w,- xx.<ly=....],~ M__——- M% J0 4" 4 y 4’ NPL (c) The moment Mm of the lamina about the m-axis. 1 2 5'1 ‘ M =§Xix1dx:——X) =3; " .3 10 o 10 N PC ((1) The center of mass (is, g) of the lamina. ’1 . X a. ‘3‘ m «‘2‘: ~10 mnsistent ‘3 «\WM above (3Q 10.‘ Determine Whether the sequence converges or diverges. If it converges, ﬁnd the limit. [10) (You need not show work for this problem). (a) an = cos mr '1,1,-—1,1;il..,, _ «a (b) an‘1+n ' bum (—x‘ :1le i... X690 114% X—MM .1. x ...
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Solutions-166E2-S01 - MA 166 EXAM 2 Spring 2001 Page 1/4...

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