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101-2005&amp;2006-2-M20-May2006

101-2005&amp;2006-2-M20-May2006 - Kuwait University...

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Kuwait University Math 101 Date: May 4, 2006 Dept. of Math. & Camp. Sci. Second Exam Duration: 90 minutes Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed Answer the following questions: ---~ x2 - 1 ,~) 1. Find tl (1) , where f (x) = --, - x 2, Use differentials to approximate: (2 pts,) 3, Find an equation of the normal line at x = 1, to the graph of x2y + sin (xy - y) = 2, I'~ d '4. (a) State Rolle's Theorem. 6. (b) Use Rolle's Theorem to show that the graph of f (x) cannot have more than one inflection point in [0,1] . (1 pt.) = x4 + x3 - 3x2 + x + 1, (3 pts.) -... 5 .. i/ The radius of a closed right circular cylinder is decreasing at a rate of 1 em/see and the height is increasing at a rate of 4 em/sec. Find the rate at which the total surface area of the cylinder is changing when the radius is 6 em and the height is 10 em. (4 pts.) \ \ .~' " 2X2 - 2x + 1. 2x - 2 6 - 4x y 6. Let J (x) = 2 ' and gIven that f I (x) =...: 3 and tl (x) = .' x x .. x ~ (a) Find the vertical and horizontal asymptotes for the graph of f, if any.

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101-2005&amp;2006-2-M20-May2006 - Kuwait University...

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