mat127practicefinal

mat127practicefinal - MAT 127 PRACTICE FINAL (1) Consider...

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(1) Consider the initial value problem y 00 - y 0 + 3 y = 0 y (0) = 1 , y 0 (0) = - 1 . Assuming the solution to this initial value problem has is the power series y = X n =0 c n x n , fnd all the coeFecients c n ±or n 6. (2) Use the seperation o± variables technique to solve the initial value prob- lem y 0 = yln ( x ) y (1) = 2 . (3) (a) Use Euler’s Method with step size 1 to estimate the value y (3), where y denotes the solution to the initial value problem y 0 = y + x 2 y (0) = 1 . (b) Sketch the direction feld ±or the di²erential equation given in part (a). (4) Determine whether or not each o± the ±ollowing sequences { a n } con- verges. I± the sequence converges, then compute the limit. (a) a n = 2 + ( - 2 ) n (b) a n = ( n 3 - n + 2) / ( n 2 - 3 n 3 ) (c) a n = 3 n /n 4 (d) a n = n 2 /n ! (5) Use any method to determine whether or not each o± the ±ollowing series n =1 a n converges. (a)
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This note was uploaded on 04/26/2008 for the course MAT 127 taught by Professor Guan-yushi during the Fall '07 term at SUNY Stony Brook.

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mat127practicefinal - MAT 127 PRACTICE FINAL (1) Consider...

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