**Unformatted text preview: **t ) is continuous at any point on [ a, b ] except possibly a Fnite number of points (namely, points of discontinuity of f ( t )). EXERCISES 7.3: Properties of the Laplace Transform, page 365 1. Using the linearity of the Laplace transform we get L ± t 2 + e t sin 2 t ² ( s ) = L ± t 2 ² ( s ) + L ± e t sin 2 t ² ( s ) . ±rom Table 7.1 in Section 7.2 we know that L ± t 2 ² ( s ) = 2! s 3 = 2 s 3 , L ± e t sin 2 t ² ( s ) = 2 ( s − 1) 2 + 2 2 = 2 ( s − 1) 2 + 4 . Thus L ± t 2 + e t sin 2 t ² ( s ) = 2 s 3 + 2 ( s − 1) 2 + 4 . 396...

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