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BC_MAC2233_2010_0708

# BC_MAC2233_2010_0708 - MAC 2233 Quiz 5(Take—Home SHORT...

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Unformatted text preview: MAC 2233: Quiz 5 (Take—Home) SHORT ANSWER. 1|Write the word er phrase that best completes each statement or answers the que CLEARLY in the space previded. Give the exact answer. Differentiate implicitly to find the slope of the curve at the given peint. 1) 3:3 + 3er + x2 _ 31\$ 2 0; (1,1) _ ,:_ l.— 'xz-f-j 41] +2:c— @213 ,1 9‘: ﬁx fag +2(:)(.)j+2(r)—rgm‘§:w x +ﬁ+2+¢2réj ~ Calculate dyfdt using the given information. 2) :24? +3.2; dxfdt=12,x=1,}-'=(J i + a — J 2 d ? ig‘f’g —~ -~ A 6" df[:—j \- if; + ’7 (6“ a“) [X (H7) (97‘ hat—g) f". x, 31‘ u’v-uv’ V 2153,35 +2y5ﬂ1 ( j E.— I' at 9% : ix 4 \ﬁ' 2x9rt—1-g7ﬁ DOE]: X‘F'lj L415): 1—3 m 335. —{2’ Kz: 7:0 .r f " uyﬂriWJriﬁﬂ v(£)=§’ﬁ<~_ jg (if J13 3‘": dt 24.6110 D3 (1 EB( it} _. a 1. ‘ 5 {>1— +i¥J 6 ﬁt) 11 “J Jr AJC (I any. = 2(002) Hm}?! MAC 2233: Quiz 6 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the I Find d}?de by implicit differentiation. 1) x3+y3=5 ﬁfxvtﬁé r2 1". A) _ _.-_ X2 RaTes of Change and RelaTed RaTes (Sec. 2.3 <94 2.81 There are Twe basic Types of raTes of change: 1. Average raTe of change. 2. InsTanTaneaus raTe of change. 1. Average raTe of change an The closed inTervaI [a, b] (ThaT is from x = a Te x = b) is "in"? we = ﬁe-ﬁm 19—11:. 2. The insTanTaneeus raTe of change aT x = b is The derivaTive aT b: f'(b) PasiTienI Velaci’rg and Accelera’rian: 1. The pasitian of an ebjecT is iTs direcT disTance in a parTicuIar direcTien from a reference painT. 2. The displacement of an ebjecT is iTs change in pasiTian. 3. The velacitjg of an ebjecT is The raTe of change of its pasiTian wiTh respecT Te Time. - If The veleciTy is pesiTive, Then we are moving in one direcTien (selecTed before) and if The veleciTy is negaTive Then we are moving in The eppesiTe direcTian. - Speed is The magm'raa'e sf rhe irefacr'ry Speed is never negaTive. 4. The acceleraTian of an abjecT is The raTe of change af The velaciTy. Suppose ﬁt) is the position of on object offer time t. Then instantaneous velocity, v(t) = f'(t) [Fir-st derivative of position] Acceleration o(t) = v'(t) = f' '(t) [Fir's’r derivative of velocity: 2nd derivative of position] “Wage Mm; ow It“ +D ma.- x/Au: Rio—4(a) ell-Pm] bee _ XZ‘XJ Ex. 2.3 (p. 11?) #15: The height s in feet after time t in seconds of a silver dollar dropped from the top of the washington monument is given by: S : __[L’t1_+ (a) Find the average velocity on the time interval [2, 3]. (b) Find the instantaneous velocity when t = 2 and when t = 3. (c) How long will it take the dollar to hit the ground? (d) Find the velocity of the dollar when it hits the ground. @J PW e “400%: “M: iii a: SC%)—\$(e>— Len- M7 lag—“t1 3-2 a \iij‘] : - 30 “gt/Se: Waﬂﬂm V4941? V06): Sh): ‘3215 Vol): "33(2): hég‘ ‘Ft/‘Sec we): 4’20): - 4:; s“. (C) l'l'a‘jl‘d ‘J jaw;on s: 7 ‘pt/ 0 5° O=—lét1+sss——J _S.59='/étl “9 In d He: NM { )Vdﬂqh a} 5”“; Wm) “‘32(s.3ﬁ):—nso.s Weta/5.“; 3M5“ Related Rates Nate: - Unless athervvise stated: we assume that rates are with respect ta time (that is: dt). - If the changing quantity is lessening (that is the value is decreasing) then its rate at change is negative. - If the changing quantity is increasing, then the rate at change is pasitive. Ex. 2.8 (p. 160) Find dy/dt and dX/dt far the given functian at the given values. Ex. 2.8 #6: The radius P cf Cl sphere is increcsin 01' c r‘c’re cf 2 inches per- minu’re. Find The rci’res of change of The volume V when (u) r = 6 inches and (b) r = 24 inches. __—_—_—_—_ Ex. 2.8 #14: All edges of a cube are expanding QT c m’re cf 3 cm per- second. How fcs’r is The surface area changing when each edge is (c) 1 cm and (b) 10 cm. QR 1‘ 2x2+7211 + 2 X1 ...
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BC_MAC2233_2010_0708 - MAC 2233 Quiz 5(Take—Home SHORT...

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