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Hayrapetyan_Test_1_Fall_2007

Hayrapetyan_Test_1_Fall_2007 - TEST 1 Calculus II PALL 2007...

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TEST 1 Calculus II, PALL 2007 Name: 13 ItA J Show your work/steps. x4 Problem 1. (2.5 pt) Find the deriva,tivc of .r In (1 + {3)dt. 2 x .~t4 \~~ y,l.. I \+--L.~ ---- --. -- -- -- Ie" x ~ Lj ..\- l\ 'X. ) o 1
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-I ----- -_..!------- Problem 2. (2.5 pt) Find t.he average value of the funct.ioll J(x) = x2e,,;3 on the int.erval [-1,2]. I. (),).. -- --- - -------------- - IJ I ..• "2 x J -..J ""t 7 .c (')!) (\ 'I. F /-vc, ": ~ \ \1. ( ~'3\ t ",1..e., /C'I ? -x e z \ • I - z (I 3 - -3 (:-J) -t e I f V.j G q e.. ('\. . 1,\ - - -i, 'J( Lj ) Ol:2 x -=.~ .==;> X =. ~ I ''is ~l 'S .~ e -e.. \ -, , 5 e u. ciu... .- '-' - -- - -~ Gte c, \ 2
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I 1 - C) ~_~:;robl,em ,3. (2.5,'pt) Find the area of the region boullcled by the curves ~O~~ = 11~ x:3, y = ,r;), alld:c = O. h J~(\<o-,,-,,) - ,,-' J't D " J . , ~: ~ (10-(><3 o..'i (? "L :: ) (1<0 .-;(){ :s)d X o '/ :2 1\.0 -'X ~ -= )<.. '3 L)(,3 --;;; \~ 'f.,.3>,~ ~ 'f .... ~ Z. 'l f\ N'.~ =-- S (Ho- ",,3-~ '3) d>< o \ 'z. j .xx'i , \ .:::~ C:, X- -4-) c ~f(" (z) - <3(~) 1- 6 = 32 - <g 3
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7 Problem 4. (2.5 pt) Use the method of washert; to evaluate the volume of the Rolid obtained by rota.ting the region bounded by the curves x = y2 - 4 and :J: = 0 about the line :1: = 2. 1. 6J "jf.:=.. j Z _1...1 \. i - Z -- K.c .... (.(,<.J~~ , j , ? V= '3y - ~y I ~)(-: :2'iT(r1. -r,\ {)11 L{ 'i "2 -~) - z.. l "') - ...-::::'..- X='j"4 rV '\ f _ rs.. .. _" y 1- V v·" - ' - ,.."l 1) _I' " - 4 '- _ 04>'-2"'.\ ' \ ,,_ 31z ~ v· ~ 1/ '\)~ (..1,_ ~ ,)' -(,,(2-:1 '-"1.2 V \...3 1\ + I L) _ J ) jl \j ~~, 4) _ 1\ (3' 'i5-17.) (3 " - If') '\(_ 4 I - ""'3 -+
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