101-2002&2003-2-M20-May2003

101-2002&2003-2-M20-May2003 - V'f\. . c..'...

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Calculators, Mobile Phones, Pagers and all other mobile communication equipment are not allowed. May 15th, 2003 Time: 15 minutes wrath 101 Second Exam .'a".lwai t University ath. Camp. Sci., Dept. 1. Let f(x) = yX=3. Use differentials to approximate f(11.7). (4 Points) 2. Find an equation of the normal line to the graph of xy + (x + y)3 + 1 = a at x = O. (4 Points) 3. Find two real numbers x and y such that: x + y = 16 and p=xy3 is maximum. (4 Points) 4. Let f be a differentiable function on [1,3] with f(l) = 3 and f(3) = 1. Show that the graph of f admits a tangent line at c E (1,3) parallel to the line of the equation: x +y - 4 = O. (4 Points) x 5. Let f(x) = -( - )2' x+1 a) Find the vertical and horizontal asymptotes (if any). b) Show that f'(x) = ( 1- x)3' Find the intervals on which f is increasing and the m+1 intervals on which f is decreasing and then find the local extrema of f (if any). c) Given that f"(x) = ~(x - ~1. Find the intervals on which the graph of f is x+1 concave upward and the intervals on which the graph of f is concave downward. Find the point of in:B.ection(if any). d) Sketch the graph of f. (9 Points)
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This note was uploaded on 02/23/2010 for the course CHEMISTRY 0420101 taught by Professor Dep during the Spring '10 term at Kuwait University.

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101-2002&2003-2-M20-May2003 - V'f\. . c..'...

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