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# finsol - 1 Express the area of the region of the plane...

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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??? HEM-2‘ “X ”X — x. I f ~ 2 “ﬂ 1:: “ﬂux 7(qu Xx ‘317‘: _____._// mix“ & WM. 7,0“ I w KW” 76“”) )ﬁ‘ ‘7[‘ 17 “LE :Q-r'l :3 :- Jum 3&4“ “F/H‘“ MK 5. Calculate the average of the following functions over the given intervals. ii/C’ rem-1L1] (a) f(\$)=sin3a:cosa: over [0,1T/2] 1D 0 [)0 i will] (b) f(:1:) = |2—:1:| over [1,4] TWA ! Llrﬂir-AZ r , . _ 1 (M is ng hazel/>0 chug/MM b Hal-:wCol—‘O " K - l 177:" ( . _ : 395?) ugckm “(‘41)" ”L4 a} 0 ‘ 3\ i bill “3%.! 33;: :Fﬁu '0 7T Ly 9‘! (L) a~>< 52L ”753 7%)”: 70a ,L esxétf [4. L} ' ~31 r a) J/ ‘ J/ 8 er ‘—<%( 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‘ (w-fﬁ ”my? Wait: PM}? 7C : 0/ XT*é / pm _: I LIX-réN/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/”({1W-I 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 V5-e: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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