101-2007&2008-2-F10-June2008

101-2007&2008-2-F10-June2008 - Kuwait University...

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Kuwait University Math 101 Date: June 5, 2008 Calculators, mobile phones, pagers and all other mobile communication equipments are not allowed Answer the following questions. Each question weighs 4 points. 1. Evaluate the following limits, if they exist: (a) lim x 0 1 x μ 1 x +5 1 5 (b) lim x 0 sin 6 x x cos 3 x 2. Find equations of the lines of slope 4 that are tangents to the curve y = 1 x . 3. Let f ( x )= x 2 + x | x | , where x 6 =0 . Can f be de f ned at x =0 so that, f becomes continuous? Justify your answer. 4. A farmer has 200 meters of fence to be used in constructing three sides of a rectangle. An existing long straight wall is to be used for the fourth side. What dimensions will maximize the area of the rectangle? 5. Show that the equation 2 x 5 + x 1=0 has exactly one real solution. 6. Find the local extrema of f ( x )= x 2 Z 0 1 sin t +5 dt , x R . 7. Find the average value, f av , of f ( x )= | x | on the interval [ 1 , 2] . Find the point a [ 1 , 2]
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101-2007&2008-2-F10-June2008 - Kuwait University...

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