101-2001&amp;2002-3-M20-July2002ns

101-2001&amp;2002-3-M20-July2002ns - 2 x-I(~2 1 A ~ •...

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Kuwait University Math. & Camp. Sci. Dept. Math 101 Second Exam July 25th, 2002 Time: 75 minutes Calculators, Mobile Phones, Pagers and all other mobile communication equipment are not allowed. (3 Points) x + xy + 2 . dy b) Let x = 2 . Fmd d- at y = 1. y x (3 Points) 1 ( 27f ) dy 2. a) Let y = "2 - 2r, and r = 1 + tan -- . Find -d at t = 3. r t-l t (3 Points) b) Let y = yX. Approximate the change in y, if x changes from 4 to 3.9. x-2 (3 Points) 3. Find two real numbers x and y of minimum product such that x + y2 = 12. (3 Points) 4. a) State The Mean Value Theorem. b) Use The Mean Value Theorem to show that if 0 < a < b, then b-a .Jb - va < 2y1a' (4 Points) 2 5. Let f(x) = -;--, f'(x) = -2x and f"(X) = 6x2
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Unformatted text preview: + 2 x-I (~2 1 \? . A , ~ • a) Find the vertical and horizontal asymptotes (if any). b) Find the intervals on which f is increasing and the intervals on which f is de-creasing. Find the local extrema (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 point of inflection (if any). d) Discuss the symmetries of the graph of f. e) Sketch the graph of f. (6 Points)...
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