SampleTest3v1

# SampleTest3v1 - MATH 3705A Test 3 March 2006 LAST NAME ID...

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MATH 3705A Test 3 March 2006 LAST NAME: ––––––––––––––––— ID#: ––––––– Questions 1 and 2 are multiple choice, worth 5 marks each. Circle the correct answer. Only the answer will be marked. 1. At x = 27, the Fourier sine series of f ( x )= F 1 , 0 x< 1 0 , 1 x 2 k converges to (a) 0 (b) 1 2 (c) 1 2 (d) 1 (e) None of these 2. The solution of the wave equation u xx = 1 9 u tt , 0 <x< 2, which satis f es the boundary conditions u (0 ,t )= u (2 ,t ) = 0, is given by u ( x, t )= 3 n =1 sin p n π x 2 Q a n cos w 3 n π t 2 W + b n sin w 3 n π t 2 W] . If u ( x, t )sat is f es the initial conditions u ( x, 0) = 0 and u t ( x, 0) = 3 sin( π x ) sin(3 π x ), the coe cients a n and b n are given by (a) b 2 = 1 π ,b 6 = 1 9 π ,b n =0otherw ise ,and a n =0fora l l n 1. (b) a 2 = 3 ,a 6 =1 ,a n = 0 otherwise, and b n

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SampleTest3v1 - MATH 3705A Test 3 March 2006 LAST NAME ID...

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