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101-2007&amp;2008-2-F10-June2008

# 101-2007&amp;2008-2-F10-June2008 - Kuwait University...

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Kuwait University Math 101 Date: June 5, 2008 Dept. of Math. & Comp. Sci. Final Exam Duration: Two Hours 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 fi 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] , that satis fi es the conclusion of the Mean Value Theorem for Integrals.

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