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Unformatted text preview: 1. Express the area of the region of the plane bounded by the curves
y=$3+2w2—4 and y=$3+$2—m+2 as a deﬁnite integral, but do not calculate it. X3+£X£Ll == XZXR’X‘LOZ .2 X +X~ér0 2. Find the absolute maximum and absolute minimum of
ﬂ?!) = (93 + 1W — 1W3
on the interval [0, 2]. r '1/
£06) 2 ['X 4}) 3 + (X + t)%/7<' J" I) 3. Set up, but do not evaluate, deﬁnite integrals for the volume of the solid obtained
by rotating the portion of the ﬁrst quarant bounded by the curve y m sin(a:2) and the
axes in the manner indicated. (a) Rotate about the m—axis. (b) Rotate about the line 3; = —1. 4. Calculate the limits, using only techniques from Math 31A. 1:110 POWJZJ (a) £113: (I‘/11+_E__%) [[0 fowl—i3] (b) lim 25in2$+$2 sc—vO a: sin :1: { '2 ,
U’”) / a .3.“ / i/w’m "2
ilk/\(TEHX i/iitnxhﬂ ; 4'17??? HEM2‘ “X ”X —
x. I f ~ 2 “ﬂ 1:: “ﬂux 7(qu Xx
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mix“ & WM. 7,0“
I w KW” 76“”)
)ﬁ‘ ‘7[‘ 17 “LE :Qr'l :3
: Jum 3&4“ “F/H‘“ MK 5. Calculate the average of the following functions over the given intervals.
ii/C’ rem1L1] (a) f($)=sin3a:cosa: over [0,1T/2] 1D 0 [)0 i will] (b) f(:1:) = 2—:1: over [1,4] TWA ! LlrﬂirAZ r , . _ 1
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b Hal:wCol—‘O
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3 g [5%le 1" g (1‘; X69 + (1% if 6. Given the function 2 f(:r:)= $+3’ ﬁnd the local maxima and minima and determine the intervals on which f (at) is
concave up or down. 22x) 3 WWW : >2: m : Mme) :
j (Mff‘ (wfﬁ ”my?
Wait: PM}? 7C : 0/ XT*é /
pm _: I LIXréN/YvLﬂ/i 3:? 1+ éﬁ)[,.xrr?}
(X+jf :_
5119‘; 1,,ar‘%'+/2? w exit/M —: L51 5
“#777?” w 7. Evaluate the integrals. [70 [J 015711 J (a) ] $1/3 + 2332/3 dx [(0 IUD/”({1WI 8. Find the equation of the tangent line to the graph of the function f(m)=[:2\/t3+1dti tun = Siltitf M : O
L‘
a, 0 : [ﬁght—9‘) 10 9. A cylindrical container is to be constructed from metal alloys whose costs per
square foot are $1 for the top, $4 for the bottom and $3 for the side. The volume of
the container will be 200 cubic feet. Find the radius 7“ of the base and height h of the
container for which the total cost of the metal alloys will be as low as possible. a 5 goo «q
lira/LN :Tfrg‘l’i 1.1100 h : «7‘77 1— Daft — U) (Trll +(‘f)(7ﬂ»3) +(g)(a77;~ A) C (r) : gll‘l'a‘ﬁL é—lll’Vfi/E; 1A“) 3 a
r _. «W (. 0t, eL/
CM ﬁ/ent [20 Z?
" NO 1.7 law
{low V5e:f , r
L Qxeo L59)—y3 10. Prove that the equation F: has a solution, but do not attempt to ﬁnd it. .A% if“) ,0 AAA 0\ 50 [LA/W <7
14A 11 ...
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 Fall '09
 Brown

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