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101-2006&2007-3-M20-July2007

101-2006&2007-3-M20-July2007 - Kuwait University...

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Unformatted text preview: Kuwait University, Faculty of Science, Dept. of Mathematics & Computer Science Calculus I (Math 101) Second Mid-Term Test July 19, 2007 Duration 90 minutes M Calculators and mobile phones are NOT allowed Answer the following questions: 1. [2 pts.[ Find the derivative of f(m) 2 V 2st + 1 sec3(5 — 3:2) 2. [3 pts.] Show that the curves :52 + y2 = r2 and y = mm are orthogonal [meet at right angles) for all constants m 96 0, r 75 0. 3. [3' pts.] Use difierentials to approximate 7 +. (1.02j4. 4. [4 pts.] A point P moves on the curve 3; = s + 5 such that iii—:32 3 units/sec. Find the rate of change of the distance between P and the point Q(2, 0) when P is at (—5: 0)' I 5. ['4 pts.[ (a) State Rolle’s theorem. . k m if 0 S x S l (b) Letf(3:)—{2_$ ifl<zc§2' i. Show that f(0) = f(2). ii. Show that f’(c) -# 0 for all c E (0, 2). iii. Does this contradict Rolle’s theorem? Explain. 6.. [Q'pts.[ Let fix) = $279 23 (a) Find the vertical and horizontal asymptotes for the graph of f, if any. (h) Find the intervals on which f is increasing or decreasing and find the local extrema, if any. (c) Find the intervals on which the graph of f is concave upward or concave down- ' ward and find the points of inflection, if any. (d) Discuss the symmetry of the graph. (e) Sketch the graph of f. -'r Mun '3955C‘57XIWEAESJXQC—a .5230“ 1 1. _... m. 6:5. _ _~ - L 1+3 ”‘11 “:3 a): _" if}, 1:) 'EGTKggw:_ Mac.‘ ”’7 3 7. Wu!- 2;") 3;:— _ m :i? “The Cuma 'meeiq' cdr 0W ocwfim. \ QCX'Ft—X—AKH‘ QC¥\:UK3. X:\ m~dx ax:o.ol. ch+un -'=" 52W) + EEarN 0K :5 Qanaa} “5 %L\\ + 5%“QO "—1.”; Q\.o'L\‘+'"._=, %_.\_LLJ\L0.0’L'\ : 9.0%. PQL:€L:C;E_’L§L+ ($431: aria, (1+5? —; r2231“ +20: __ on? _ mew,“ air—«‘73) é s’l :7 L230“ d9 :Qwflkzfi 5W; :3 agi— : -3 wwflrs/gzc', ‘19 i. QCCB “:2 C) :_ 9C1“! “ \ 1 04—915! 1 n u- ”QCscfiz: R ‘ g :) ECQ7 VEOVCGCOF. ,n‘ {a \A7541 m. Na , Q5 53cm 1-3- MK- ckxggereA-‘olom adv x: I- an j ’um __ Qua 21.60 1:2? $74-40 is, cx Mtg: £231" ‘4“ -) Q—CX] : mk‘ud') :) MG \A—Os‘i. CO ...
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