101-2008&2009-3-F10-August2009

101-2008&2009-3-F10-August2009 - Kuwait University...

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Kuwait University Math 101 Date: August 15, 2009 Calculators, cellular phones 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 sec 3 x tan 3 x 5 x (b) lim x →-∞ 2 x 2 + 1 x + 1 2. Find f p ( x ) , where f ( x ) = x cot x 2 x 5 + 1 . 3. Let f ( x ) = 2 x + | x | . (a) Find the points, if any, where f is discontinuous. Justify your answer. (b) Find the points, if any, where f is not di±erentiable. Justify your answer. 4. Find equations of the lines passing through the origin and tangent to the curve y = x 2 + 1 . 5. Let x and y be two positive numbers whose sum is 4 . Find the values of x and y that minimize the function P = x 2 + y 2 . 6. Prove that: 4 i 1 cos 2 x dx = 3 - 4 i 1 sin 2 x dx 7. Let f ( x ) = x 2 i 0 t - 4 t 2 + 1 dt. Find the intervals on which f is increasing and the intervals
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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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101-2008&2009-3-F10-August2009 - Kuwait University...

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