1. (4 points) Find the Laplace transform F(s) = L{f(t)} for each of the following functions. (a) f(t) = 4t^3 + 6t^2 + 4t - 2 (b) f(t) = 2 sin(3t) - 3 cos(2t) (c) f(t) = 7e^{-4t} + 8e^{-2t}
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L{4t^8} = 4L{t^8} = 4\frac{8!}{s^9} L{6t^2} = 6L{t^2} = 6\frac{2!}{s^3} L{4t} = 4L{t} = 4\frac{1!}{s^2} L{-2} = -2L{1} = -2\frac{1}{s} Now, we can add them together: F(s) = 4\frac{8!}{s^9} + 6\frac{2!}{s^3} + 4\frac{1!}{s^2} - 2\frac{1}{s} For the second Show more…
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