math142 s06 quiz1 to quiz11 - -—-~ a Math_142 Quizl if“...

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Unformatted text preview: .---—--~:-.\__ (- a, _ . Math _142 - Quizl if“ No calculators, Show all of your working. Name: ‘7 l' l 5 100+ 5 1. Evaluate the indefinite integral 1+4:1: ————————~—~—dm v1+$+2m2 2. Evaluate the definite integral, if it exists: fan ‘1)25 dz: l‘l—l‘lx _ Ax V: \+>{+1xl {i\+x+ml W = 3*le (M , r‘J W W : _..,.___.. ..... (I 25 \J'V" X=U w“: \ L'X‘l) 5"? cl. " (”Wu x": l xvii"; I Math 142 — Quiz2 I No calculators, Show all of your working. Name: .' l 77 7' 743” \S‘Eetch the region enclosed by the given curves. QECide whether to integrate with respect to a: or y. Biaw a typical approximating rectangle and label its height and Width. Then find the area of the region. I 1.'2:=1'—~y2,1::y2——1. RESPEH'TD x; Page 2 @ Math 142 — Quiz3 No calculators, show all of your working. Name: 1.4:... L EH, ) ’lOD . 1. Find the volume of the solid obtained by rotating the region bounded by the curves y = 33 and y 2 J55 about the line y z 1. Sketch the region, the solid and a. typical disk or washer. 2. Use the method of cylindrical shells to find the irolume of the solid obtained by rotating the region bounded by the curves 3; 2 $3, :4 : 8 and a: = 0 about the zit—axis. Sketch the region and a. typical shell. .’1 ,- L 9: -:1-.~1.'}l.¢)flf» l V V SS 21W: ‘K.’ (““5 K \2/ Cl“ y: g {E} Hf?“ ‘5 mi»: __,_\__.e.— 4. 1"}. m2 ' 2 W 9‘ q\ Wei. (3”) :1 k1 Le “ («77$ _"~_ » {BAH-I? “r b " ° "' f 6 ;~ (16m Lima ejfié’xi "' '3'; 3 3 572‘ 1 % ii» ”I. f '2 1T 5 fl 0 “ " I L ‘ 1‘ /_, »-"""'“""‘"" ":3; 7" , a." "Nit—'- Tfi Name“ 3% 'W% U h . :2 G! n "‘ ll” NVIW' ‘6 t W __ ‘ . in get; ”H‘i '"‘"‘ " F) q.” “Hui: avg" Page 2 Math 142 - Quiz4 @ No calculators, show all of your working. Name: ‘ lL N 2004 1. A cable that weighs 2 lb /ft is used to lift 8001b of coal up a mineshaft 500 ft deep. Find the work done. W" l: Cl Cl : SODH . b l‘ “N; a . '1, goo 14*: ‘7."- V ' moon: / H; l \fl/I’i‘l’ a“ u l‘ M :30“ I ‘ E g. 7 F: m ' . . we; 3 . .37. 90“” {woo @130 c ‘ W air "L. I"\"‘ 7C0!“ 9)!) j 90014:: + 2x. cm 31cm: D 3°“ A “£990 0 1 Sb” 0‘) L) U U {EON +%]a “$00000 @090 V WW W' $130 4' 500’}- 490,420!) + 25099" 3w ' gnu ”WWW—n o a: O a: 937))003 “(aw/H {IX}. ‘2", (.19 a _. - ‘w '43) fl ('3' 333))“ 00 9......” .. 2. In a certain city, the temperature (in °F) t hours after 93m was modeled by the function 1ft Tt - 50 14 ——— (t )- + sin 12 Find the average temperature during the period from 9am to 9pm. 1 b . 5’ 3 ll ‘- “fLXDGIx. ‘0'“ a I ‘1 / IL U2 :12 J + ( .. , / 93+ “Hm”— "H- -‘ ~" IE1) “r” Wrang- er ' 11-0 05 \2. a . dfifiafifi ibit/ + H Log if] WCM-Mm ‘3‘: 1’ —-' WINNC | 0-1" “W 0 ”11-5“ Mfiz _- : [go-n. + M GA? '; J. _ _ ‘13]: “J3 L1;— 2 [w W] '2, if)“: 3 EM 2‘90?! ? TM, _ 7‘ l - — K 61% MW , ‘50 i ‘1 m M \“J Page 2 Math 142 — QuizS I No calculators, Show all of your working. Name: _ _ '2‘ 700 1. Find the formula for the inverse of the function f($) : v10 — 31' 2. Suppose g is the inverse function of f and f (4) = 5,f’(4) = §. Find g'(5). I143"? ISLQ):4 , f‘T‘W’a 3H5): m 3>_ 2 Page 2 @ Math 142 - QuizS No calculators, Show all of your working. Name: __._._'_\A - 1 Mb 1. Find the derivative of y = cos—1(ezz). Simplify if possible. l5: CM" LELXB - l 1 Cl «1‘ ‘ ~| my on 2 «---— . gr“ 2. Evaluate the integral :j 2% 0M} WNW“) ll Page 2 ch) W \‘rU H (a Math 142 - Quizfi No calculators, Show all of your working. Name: ww—fi—“—_ 1. Evaluate the integral [0035(33) sin4(m)d2: 2. Evaluate the integral U: 90315343 f moswmdm {A 53,47: n By. on; \w* jww O\ 25g mg. X a as} J ‘ 1, 531MB) J ‘15-‘51an m \r: x U : CK dd: 6““ X _. fl ' :1. LBW. Eimbx‘ ejkxnbx cbé dwgd“ CW (OS 30W. . qr.) gm E3“; S fl I _..__._.—_..-«- WW _+——~»~—-' ‘__.__..— Page 2 Math 142 - QuizS No calculators, show all of your working. 4 Name: 1. Evaluate the integral using the indicated trigonometric substitution. Sketch and label the associated right—triangle. 1 ——-——-~———d$ 1::33eczz: 21/ 2_9 ’ m 33 x1: amtx ox: . \ : ”‘T'FL‘ ah: -, ‘ ”“1 I ‘12?“ mfiifitx'q amtx (rem—i) ' ”tilt‘x "MM 1L l\ l _ sj EEK/2’3; ctx m! ' " Waist u: 2}“?! do: gtcx mfix 0‘ x 2. Evaluate the integral x ‘J" xzflr r” 91* (Aw- «m dx “Mr , X M L i r -mfi—J ’ “7:" .—---' — :‘ '"‘ 3 UJfb-F 1' j w w! ’Zj W ”N am] \X/llc’ ‘11 x}— Page 2 Math 142 — Quile No calculators, show all of your working. Name: _" , ' Maj H3004 - _ 1. Write out the form of the partial fraction decomposition of the function. Do not deter— mine the numerical values of the coefficients. (a) m H} w— 1‘) xii-x} w .2 LYHBUHU Nicki -l (b) 2:4 )ll‘l fi- YE: + ”54—1 .LKfiDsz'lBZO-(ZB LEI—:1) _ “if? AVE 4% ’( Q: _ r .. j -r ..... LXL+'3{~<‘1)(>&\) x?“ X“ X~H X\‘ xq/ t4+t2+1 ’ pm» f“ o 4;" 2 2 2 : TEL—D « 3-" (t +1)(t +4) 1 El flag {ff-N)" 2. Evaluate the integral 1 ——-——-dm f m/ 4:1: + 1 (Hint: make an inverse substitution to make this into something for which you can use partial fractions.) 1 U: LZIQM ul=uox1 m ‘1 EH : MU'D kPJLu’rD V" 1 0—723 B~f U9"? fist-113* Pr?" -1 . ’— C‘LC'L .u"" r‘ U-r} wt 'l \xmem‘w 5*” , 3‘] ' .t 4'- b Ham-11 Wm H" ‘l We Math 142 — Quizll @ No calculators, Show all of your working. Name: _._.._.._,__H. M 7 Cl '2 339‘ 1. Determine wether the integral is convergent or divergent. Evaluate it if it is convergent. 1 1 [002—de um “I. _ _I_ _ W" ’3 f2.——~U\j {w — O @0meth 2. The integral [:0de is improper for two reasons: The interval [0,00) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as the sum of two improper integrals as follows: immdmffii‘amffidmde (Hint: you might want to use an inverse substitution to evaluate the integral... and you should have an inverse trig function when you integrate.) a"; - ’1. \ \ a} ‘X X4} (‘1, -‘l )Wfld‘fl+{_fl--\»—w ._ {Mix‘ld’f O WU“) \jfl’ilfiu Y {114; I -. .,\_ .- \ 1w" 1 251cm Page 2 ...
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