m238sp05t4 - 3 if t 3 Rewrite the function in terms of the...

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Mathematics 238 test four Friday, June 10, 2005 please show all your work to get full credit for each problem 1 . Find the function which corresponds to each Laplace transform: ( a ) 2 ( s + 4) 3 ( b ) s + 3 s 2 - s - 6 ( c ) 6 e - 2 s s 2 + 9 2 . Simplify each of the following: ( a ) Z 0 ± e - 3 t cos 4 t ² e - st dt ( b ) t 2 * t 3 (convolution) 3 . Sketch the graph of the function f ( t ) = 3( u 2 ( t ) - u 4 ( t )) + (7 - t )( u 4 ( t ) - u 7 ( t )) 4 . Given the function g ( t ) = 0 if t < 0 1 - t if 0 t < 2 t - 3 if 2 t <
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Unformatted text preview: 3 if t 3 Rewrite the function in terms of the unit functions u c ( t ) Calculate the Laplace transform of this function. 5 . Use the Laplace transform to solve each initial value problem: ( a ) y 00 + 2 y + y = 4 te-t y (0) = 0 and y (0) = 1 ( b ) y 00 + 2 y + 10 y = ( t ) y (0) = 1 and y (0) = 0...
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