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101-2005&2006-1-M20-Dec2005 - Kuwait University...

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Unformatted text preview: Kuwait University Math 101 Date: Dec. 15, 2005 Dept. of Math. 85 Comp. Sci. Second Exam Duration: 90 minutes Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed Answer the following questions: 1. Use differentials to approximate 6/159. (3 pts.) 2. Find an equation of the normal line at as : U, to the graph of sec2 (11' + 5:) + sin (my) -I— y = U. (4 pts.) 3. (a) State The Mean Value Theorem. (1 pt.) (b) Use The Mean Value Theorem to show that (1+$]%<4+:—:(r—7), foreverysr>7. [Hintz take f (x) : (1+ I) wlM (3 pm) 4. A plate in a shape of a square is heated. If the area A of the plate (in cmg) after time t (in hours) is given by A=\/1+t3, find the rate at which the sides of the plate are changing after two hours. (4 pts.) 4(4—I) :c (32: - 8) (I — 2)3 (I 72f I 8(55—5) 5. Let f(sc) z (SC—2Y1. and given that f ’(ar) 2 and f”(a:) = (a) Find the vertical and horizontal asymptotes for the graph of f, if any. (b) Find the intervals on which f is increasing and the intervals on which f is de— creasing. Find the local extrema of f, if any. (C) 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 the minimum values of f on {3, 5]. (10 pts.) 00 CO ...
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