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Math_121_April_2005

# Math_121_April_2005 - THE UNIVERSITY OF BRITISH COLUMBIA...

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THE UNIVERSITY OF BRITISH COLUMBIA Sessional Examinations.April 2005 MATHEMATICS 121 Closed book examination Time:2 1/2 hours Calculators are not allowed in this examination I-[21] SHORT ANSWERS QUESTIONS Each question is worth 3 marks, but not all questions are of equal di clty. Full marks will be given for correct answers, but at most one mark will be given for in- correct answers. Simplify your answers as much as possible. a) Evaluate R ( x 2 + e 2 x ) dx. b) Find the average value of sin x on rthe interval [0 , π ] . c) Find lim n →∞ P n j =1 1 n sin 2 ( j/n ) . d) Find the general solution y = y ( x ) of the di ff erential equation y 00 2 y 0 + y = 0 . e) Find the general solution y = y ( x ) of the di ff erential equation y 00 2 y 0 + y = x. f) Evaluate R 0 (1 + x ) 3 dx. g) A continuous random variable X is exponentially distributed with a mean of 4. Find the probability that X 8 . In Questions II-IX, justify your answers and show all your work .

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Math_121_April_2005 - THE UNIVERSITY OF BRITISH COLUMBIA...

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