MTH132-Test3-Sol - Page 1 2008-1 l-6 Name(Print Clearly Student Number MTH132 Section 5& 18 Test 3 Instructor Dr W Wu Nov 7 2008 Instructions

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Unformatted text preview: Page 1 2008-1 l -6 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Test 3 Instructor: Dr. W. Wu Nov 7, 2008 Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [4 pts each]. Find limits of each of the following 3/5 . x — l (a) 11m 2 ,3 A‘—>l x ’ _ 1 w ‘6 i f mt 4; v m a E“ if: g XWW l’g’ if 7:14;.” “,1; iwx when“ i g ~ A} («gr 5. )1 2 J X; y; g» .t 4X“? ’3‘ e, 3 X {Ni/K X 9“: J: «3/; ,«m M“ “T” Mew?“ 524;; x, a ‘W i’" {a / J {mg/jifi ‘1"? X {Millwiffim :47 ii} K x f t; g (2“ I :1; . x — 2x2 —— 3 (0) 11m functions. a" (grayrx - 1”” 232‘ I ("mix a ? i; i i «4, *“”“‘:‘“:'°’”‘ '- KW" “:Wwi‘?‘ ~62 G 5‘: fife) 4: L i A ’1 IF 3 M R71. ‘ 1 1M wmmmmn ~w Page 2 2008—11—6 2. [4 pts each]. Find indefinite integrals. (a) [ow ” + 3x2 — 2)dx A ‘v‘ '1: ' . i 2/5 ::> i 7’ 3»: ‘ - , ~ ‘ » , A . if, M M ‘i :3“ is m,» 2x: x «+ ,q 1+ 2x, w“ ,2 3:; «S it? «UAW ’ i 4 M4; ' - w, m r ¥ “ i i f I ““ M w Y " x 5 " I“ V em. J m ‘ «1 f M w a“ “2 '3 ‘" a" o I] 7 {L ’f - u a“, L k I K“ .3 :1 if {J r t i ' t « ,, , ‘ M ,i r» f H; 2:; $350!; > it?! “1 3“ 5 f “5/1"? erg 5, ~ » ‘ -~~ {J 5W, we feérif : x} e‘ w- {98‘ d ,, i . 3. [8 pts]. Solve initial value problem: 2:: = cos(7l' - x), y(0) = 1 . i4? (1. \» i X r» M f {I if If my} \i ’“~ x" ‘1 \ W x! 3 ~ ‘ m a ,f e 3 5” ’1 B‘ K i1: «is *5 if < %” “ta; 5.! {I i 9 4. wk L t Mi“ 3 x * 1V, 1 1 4. [iOptS]. Letf(x) = x+—, [5,2]. x (a) Show that f(x) satisfies the hypotheses of the Mean Value, Theorem over the given interval. ; i’ ’1 fl if! g s f 5' x " ,r ~ , 1 Es» .5; d'gfiuf» Page 3 2008-11-6 f(b)-f(a) b—a (13) Find C which satisfies the equation of the Mean Value Theorem: — ' ’ on i —f(6)a [222} Mi: ~ M gi’j} ,iMMmrwmmmnwfifm-Amé-v _ “M, {v}! Wm #2 _ I) 5 [1219123]. Letf(x) Zzg—E? (Note that fv(x) : (x “.6333 and fu(x) = ) (a) Find the intervals where f is increasing or decreasing. <3 5 3;” We JV {i i {:75} I x (b) Find the intervals where f is concave up or concave down. 77> 5:? '?L f ix; ’31 ““' “7"” (d) Find the equations of all asymptotes. V'a»«““‘f‘f(‘cxz€: Sigifwfl’i’iv 7" g , ii ----- '~ “Q” ’5’"? 2 M '3 if” Cw ,I’ r :2 Page 4 2008—11-6 6 [10 pts]. A rectangular bOX With volume 18 cubic meters is to be built with a square base and NO top. The material used for the bottom panel costs $2 per square meter While the material used for the side panels costs $1.5 per square meter. Find the minimum cost to build such a box. 33mm w a», xi“ ~ A T3517 g '1 "‘, \ .MM » {e A 5“ 7. [10 pts]. Use Newton’s Method to approximate «I 15 . (a) Construct a function f (x) such than/lg is a root 0ff(x) = 0 wan. 9» "fr ; “.v. ‘ l 3' t (Z V ‘ " L w “ " i 54:? f L: v: if A [79“ 5‘ aw“) i' e’ v I, If") ‘ f - r“ i '4 p 9”" WM ‘- w rs, A» 1 W“ W pl M N t ’ e’ i A“; f .1}; Q ,t; K ,2 >6 ; f a :; ‘)< w w - mmmwfiw «M w : a J i :3 ‘5 x L 1 X f m vi; W ...
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This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Test3-Sol - Page 1 2008-1 l-6 Name(Print Clearly Student Number MTH132 Section 5& 18 Test 3 Instructor Dr W Wu Nov 7 2008 Instructions

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