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101-2006&amp;2007-2-M20-May2007

# 101-2006&amp;2007-2-M20-May2007 - Kuwait University...

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Unformatted text preview: Kuwait University Math 101 Date: May 3, 2007 Dept. of Math. & CS 2nd Exam Duration: 90 min. Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed. Answer the following questions: 1. Use differentials to approximate (0.918)”, . [3 pts.] 2. a) State the Mean Value Theorem [1 pt.] 13) Let _ x + 1 ﬁx) _ x —1 ' Show that there is no real number :2 such that 1T2) -f(0) = 2f’(C)- Why does this not contradict the Mean Value Theorem? [3 pts} 3. A metal in the shape of a right circular cone, whose height is twice its radius, is being heated. If the radius is increasing at a rate of 0.001 cm /SCC., ﬁnd the rate at which its,volume is increasing when its radius is 2 cm. [4 pt5-] 4. Use implicit differentiation to ﬁnd y”, if x2 +y4 = 16. [3 pts.] 5. Let ﬁx) : 3x(x a wg-ﬁ be deﬁned on the interval [4,2]. Find the absolute maximum and absolute minimum off. ' [3 pts.] _ x2 — 9 6. Let ﬁx) _ 2x4. [8 pts.] a. Find the x and y—intercepts off. b. Find the vertical and horizontal asymptotes to the graph off, if any._ c. Find the intervals on which f is increasing and the intervals on which f is decreasing, if any. d. Find the intervals on whichf is concave up and the intervals on which f is concave down, if any. e. Sketch the graph of the function f. Total [25 pts.] 00 90 Torah 25pts ijhN-EIAJFM ﬂ'l *{CV'I‘J 1" "iv, 1 tf’f|j§ﬁ[ I :7 *‘fC'? (3:?)lo 2: ‘F‘OCO'ﬁg‘ : ‘_ig(ﬂo,02 .: \,'Z (92- lo) satin-wad a; Lac. MU t. 1 Lb] .g‘ (m : _ 2 41(1) 4(0) —,a 34-1qu 5.2.4960 I A L ' .— ;}i._ -_—-. (~— 2 :4 5M“ 1'. mi” 3 _ , LI -— (CL-n? Q \) 2) P053 if”; VLO‘: CH1. (3)23‘ Q3 V‘ﬁé—gﬂ'ﬁYL‘Lgk where {@294er V: ‘gﬁfmﬁ‘; 3U I r_ A a. 2:1? v13; .7 grr(o.oou c-MB/Arc- 6%. ix: + 43}? “if; ‘l 2).: .1 ._ ,2: 3 ’ " #1133" 1133 an ﬂ_[m{5.i — xZ'é 311‘] ' #36 _ __ 6Y3? {4:331} # — ﬂaw/6;» ~ J - “ Sx#S— C‘d ‘ N 3- ‘ 5/ ‘5 @S— 4(ch - LXFWESWB , Mad? 0 311 3 C 46¢} "If Haifa .ﬂ 1- '“ W“ I q 3Q 003' 533 9 ' L 2, ,8: a mm 1 3(q { @ 3*\WMQ-k+ (Ola/Q.) wL—MWN (tjno) ® 34:7. U-ﬁr ‘ Mo ko‘vxll'ov‘l'ofl g 3 = 2.“ "WW; + (9 % (w erml C00 W04 T» ﬁS/(x—zﬁ _+—-.; '1 OO 99 ...
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101-2006&amp;2007-2-M20-May2007 - Kuwait University...

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