101-2003&2004-3-M20-July2004ns - loosing shape at a...

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J ~, Kuwait University Math 101 Date: July 22, 2004 Dept. of Math. COIUp. Sci. Second Exan1. Duration: 75 minutes Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed 1. Use differentials to approximate vTI +.yD. (3 pts.) 2. If 2 (u - 1) y = u2 + 1 dy 7r and u = sec2 x + 1, then find - at x = -. dx 4 (4 pts.) 3. Find an equation for the tangent line to the graph of y2 = x3y2 - xsiny at the point P(l,7f). 4. (a) State Rolle's Theorem. (b) Show that f (x) = x4 + 2X2 - 3x + 1 has exactly one critical number. (4 pts.) (1 pt.) (4 pts.) 5. A cone of ice Crealll whose altitude is three times its base radius, is melting, without
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Unformatted text preview: loosing shape, at a rate of 0.3 cm3/min. Find the rate at which its altitude is changing \vhen its radius is 2 em. . (4 pts.) 6. Let f(x) = x3-6x2 + 9x-4. (a) Find the intervals on which f is increasing and the intervals on which f is decreasing. Find the local extrema of f, if any. (1.5 pt.) (b) Find the intervals on which the graph of f is concave upward and the in-tervals on which the graph of f is concave downward. Find the points of inflection, if any. (1.5 pt.) (c) Sketch the graph of f. (2 pts.)...
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