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101-2003&amp;2004-1-M20-December2003

# 101-2003&amp;2004-1-M20-December2003 - Kuwait...

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Kuwait University, Faculty of Science Dept. of Mathematics Computer Science Calculus I Second Mid-Term Test Time: 751nin. Decelnber 18, 2003 Calculators, Mobile phones, Pagers and all other Inobile communication equipments are NOT allowed. Answer the following questions: 1. [4 points] Use differentials to approximate sec2( 44.9°). 2, [4 points] Find an equation of the tangent line to the graph of sin3(xy) + Jr = Y + x at the point whose y-coordinate is O. 3, [2+3 points] (a) State Rolle's theorem. (b) Let f(x) = 3x + ~(x - l)~ + 1. Show that there is no c E (0,2) such that fl/(c) = O. Explain why this result does not contradict Rolle's theorem. 4, [4 points] Find the point on the curve y2 = 2x that is closest to the point (1,4). 5, [4x2 points] Let f(x) = (X~l?' (a) Find the vertical and horizontal asymptotes for the graph of f, if any. (b) Given that f(x) = (x~~)3' Find the intervals on \vhich f is increasing or decreasing. Find the local extrema, if any. (c) Given that

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101-2003&amp;2004-1-M20-December2003 - Kuwait...

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