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Unformatted text preview: 1. Suppose y = cos (a: sin (232) + 2:”). Find 5/ (12 points). _ ‘ 2 2 la, (2 1— "»(x’ +2x)
\/l(»<)= 5w’1()<5m(><)“)‘)<2K 5 K) g ) 2. At time t, Bob the particle is at position 23(t) = t4 — 6123 + 15%2 zero acceleration on precisely two occasions; Find these times (8 points) and ﬁnd the velocity at each of those two times (4 points). (Note: this question asks something
different than the practice exam’s problem 2.) V2x’1qe?r(t{1+2qé~7 — 7t+ 2. Bob has a : (1&2—36€+2'~( = 11(tld3ts'2) 2’1(€“’)L“"L)
So am :7 ‘t" °r i=2
V(l):qfg/+Z‘{‘7 ‘5 up): WKJI‘ZV +2JI‘Z—7 =’ 3. Suppose ﬂat) is a cubic polynomial, i.e. f(9:) = cm:3 + 5x2 + cm + d for some a, b, c
and d. Further, suppose f(0) = —7, f’(1) = %, f’(0) = 1 and f’”(7r) = —6. Find f.
(i.e. solve for a, b, c and d). (12 points). ¥(O):*7— :7 d‘=‘ (K):30kxz+2.éxrc, 51’(o)=r =7c=l gmbql Gal FN/(TF): _ :7 Q:—[
‘(x)‘=‘3><‘+llo»<+l % $3799“
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3 '29 "J 6
'7.
39M: “ng‘ Ex; W"? 4. Find the equation of the tangent line to % +Sin(:c+y) = —1r at (7T, 7r). (12 points). d
{L (5X31fo z‘ih cos—(www =0 3
TI d
y
; .33 (3(~n9 +73 (1%)HCMOJW’LEEFO
I l 0‘ — 41‘qu
I ~3+31¥+ Erk~Offo 2—dx /
5—0 if] /
dx: l——— d2
5. Suppose a: = sin(:ry). Find a formula for —y dch
I: c©5(><y) (v 5% W) I * YCCJS (Ky) in terms of x and y. (12 points). ><COS’(><\{l (W __— "XCO5 (KY)( dx Mﬂl (Cos (it/2:_V._><__g____w_;,,,, XL cosky) : ~ XC05(><7) (X(I Ycaﬂxvn ” VS‘I" (XYM
“ 0 — 5 (*Y.)_X§_‘,"_,("VJ “ 7‘ 5"“ W H
_— “vs ,# r — n. .. 6. A 5 m long ladder leaning against a building is slowly starting to slip. If the base of
the ladder is sliding away from the building at 1 meter per minute, how quickly is the
top of the ladder sliding down the building when the base of the ladder is 3 meters X 2X 3—:127 (337:;— ’ 56
x%:~7§,m
Le. 4M9 [qclpr (S glidfmj clown @ 7. A pebble falls straight down from a bridge into the bay causing a splash. Concentric
circular ripples in the water Spread out from the pebble’s point of impact. If the radius
of the rippled region is expanding by 25 011)] sec, find the rate at which the area covered
by the ripples in the water is expanding when the radius of the disturbance is 5 cm. (14 points). { _
(J74 9:": “Ff5‘25? 8. Use differentials/ tangent line approximations to approximate cos + .01). (Unsup ported answers will receive no credit.) (12 points).
Tr U5 )
y : (:03 X ( "é" / 3
l . I : F‘ 'L
y 1‘ ~ 5:0 K Y 6 l
J? .x ,1 ( II J
y F — a X w G
71:"; “2(X‘é1) ...
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 Summer '08
 Any
 Calculus

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