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101-2007&2008-3-M20-July2008

101-2007&2008-3-M20-July2008 - Kuwait University...

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Unformatted text preview: Kuwait University Math 101 July 19, 2008 Math. 8:: Comp. Sci. Dept. Second Exam Time: 90 min. Calculators and Mobile Phones are not allowed. 1. Use difl'erentials to approximate: sec(46°). (3 Points) 2. Find an equation of the normal line at :1: = 0 to the graph of y3 + ysin(:c) * ces(cc'y2] = O. (4 Points) 3. A spherical ball made in steel is heated. If the surface area A of the ball (in cmZ) after time t (in hours] is given by A=\/t2+t~4, find the rate at which the radius of the ball is changing after four hours. (4 Points) 4. a) State the Mean Value Theorem. (1 Point) b) Use the Mean Value Theorem to show that: (3 + :rfi < 2 + -:;(m — 5), for every as > 5. (3 Points) —235' . r _ ‘2 H — 4 m+lsandgw€11th3~t f (1‘) _ (Id-U2 and f (3;)~(w+1)3. 3) Find the vertical and horizontal asymptotes for the graph of f, if any. 5. Let f(z) = [3) Find the intervals on which the graph of f is increasing and the intervals on which the graph of f is decreasing. Find the local extrema of f, if any. 1:) Find the intervals on which the graph of f is concave upward and the intervals on which the graph of f is concave downward. Find the points of inflection, if any. d) Sketch the graph of f. e) Find the maximum and minimum values of f on [1,2]. (10 Points) 00 CO Hakka-km / Sew Hidorcnn Ju\-—3 \‘517—008 5:: Lué‘] 1: flab—*5") + saucer) GnLLuB‘W [125:0 :: JCS. + 42?. O (”Ab 71:0: 33_l:0 d3:\. ”-53" ‘3‘ + \j Cbsx _\_. am» \5‘ + Sme—f-x [2x3 U§+ $1130 “Ma siaPe =8 £2;qu ‘EML aficflo,fl In m ..__L " '3. :) VES¢ Ska?fiofi YE: WHO—p €0.42. oeron} £4 mL-_-_3 - Wong-«ff; can eanJnmo-SYE: “9me QML £4 : 3x+\, ("A : qmrz. (A: t1+\-_-:+ at _._ Eff» a: Gig , aha—4 t LS 32-. 2'. 87: _‘—.__ i 6+1?” 8 M: t— alct— (A ‘ $515.. “is can/hm. —:— ‘L‘WFZE 6)ch 0““ _ i ‘c _ B “'5 \0\ End: {vs-ax} m 125,563. . 9 :5 “Nov! om C5913 - 9 cs déggue—Jcmi‘ifi anLEpd god :_ _...‘_.._ . __ ’ 3L3+x1u3 ”b: HAf-I.‘ E C {n (8)x\ agucA beagl— ‘ _ €00 _ gigs“) fir.“ ' “W“ ._ .L. ‘ _ R'%+><3"5—2 ‘ ' _> 3 LB—x-cfilla " x-5 ’ C73? \%+cvrs<' 2:» Lacuna +1 5 (sir—fig 2) {3+X‘1‘3< 1+‘LLQX-TQ on v.9: bun ‘1‘” ::CD ;_ »\ , m X4-\¥7\+5 :-;>»< \3qu'A. IL‘LCX' UM .._- 12>: : ,3" :2.) S:-—1 A), Q \.'\'-Q Xa‘tco 7(.+\ b‘ 4%‘m: ‘1 C‘ 9%“ : CM 63} ‘WCEL woo-(.1 EL\\—;_\ ...
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