101-2002&amp;2003-3-M20-July2003

# 101-2002&2003-3-M20-July2003 - it University ~. &....

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1. Let f(x) = jX. Calculators, Mobile Phones, Pagers and all other mobile communication equipment are not allowed. July 31st, 2003 Time: 75 minutes Math 101 Second Exam it University ~. Camp. Sd. Dept. a) Find dy at x = 9 with 6.x = -O.L b) Use differentials to approximate f(8.9). (4 Points) 2. Find an equation of the normal line to the graph of y = x2 + x sin y + % at x = O. (4 Points) 3. Let x and y be two real numbers where: x - y = 20. Find x and y such that P=x2 +y2 ... IS mmlmum. (4 Points) 4. Let f(x) = ~, a = -1, and b = 8. a) Show that there is no point c in (a,b) such that . "';'-. t(c) = f(b) - f(a). b-a b) Explain why the result in part (a) does not contradict the Mean Value Theorem. (4 Points) .J. Let f(x) = 3x2 - 1 x a) Find the vertical and horizontal asymptotes of f (if any). b) Show that t(x) = 3(1 ~ x2). Find the intervals on which f is increasing and the x intervals on which f is decreasing and then find the local extrema of f (if any). c)

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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&2003-3-M20-July2003 - it University ~. &....

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