101-2008&2009-1-F10-January2009

101-2008&2009-1-F10-January2009 - Kuwait University...

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Kuwait University Math 101 Date: January 20, 2009 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 2 p 1 x 2 4 x 2 4 P (b) lim θ 0 2 sin θ sin 2 θ θ 2 2. Let f ( x ) = x 2 k x 2 + 1 , if x 0 , x 3 k + 1 x 2 + 2 , if x < 0 . (a) Find the value of k such that f is continuous at x = 0 . (b) Is f continuous at x = 3 ? Justify your answer. 3. Find f (1) , where f ( x ) = 1 + x 2 x 3 x 4 + 1 . 4. Find all numbers c that satisfy the conclusion of the Mean Value Theorem, of the function f on the interval [ 1 , 2] , where f ( x ) = x 3 2 x. 5. Show that: i sin 3 x cos x dx = 2 7 (cos x ) 7 / 2 2 3 (cos x ) 3 / 2 + C. 6. Evaluate: 3 i 0 3 x dx + 2 i 2 x 3 cos x dx. 7. Find the
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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&amp;2009-1-F10-January2009 - Kuwait University...

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