101-2005&amp;2006-2-F10-May2006

# 101-2005&amp;2006-2-F10-May2006 - Kuwait University...

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Kuwait University Math 101 Date: May 30, 2006 ~pt. of Math. Camp. Sci. Final Exam Duration: Two Hours Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed Answer the following questions. Each question weighs 4 points. 1. Evaluate the following limits, if they exist: 1 .1 - - 3 (a) lim tt _ 3 t---+3 sin 7x (b) ~~ 3x4 _ 5x . 2. (a) State The Intermediate Value Theorem. (b) Let f (x) = x4 - 7x + 2. Show that the equation f (x) = 0 has at least two distinct roots in the interval [0,2]. 3. Determine whether f (x) = x3 + 1 satisfies the hypotheses of The Mean Value The- orem on [0,3], and, if so, find the numbers c satisfying the conclusion of the theorem. 4. Given that P = 2x2 + 3y2 and x - y = 10, find x and y such that P is minimum. 5. Evaluate: j sIn x dx. (a) (3 + cos x) 2 2 2 j 5x dx. (b) V2x3 + 9 o 6. Show that if f is continuous, then 1 1 j J (x) dx = j f (1- x) dx . o

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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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101-2005&amp;2006-2-F10-May2006 - Kuwait University...

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