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MacLaurin Series And Laplace Transforms : Absolute Convergence

Find MacLaurin Series for the given function f. Use the linearity of the Laplace Transform to obtain a series representation L(f)=F(s)
Determine 5 values for which the series converges absolutley (and uniformly).
Also show the Laplace transform exists, i.e. that it has exponential order alpha.
Here are the functions.

A) f(t)=cosh (bt)
B) f(t)=cos (bt)
C) f(t)=t sin (bt)
D) f(t)=sinh (t)
_______
t

Solution Summary

MacLaurin series And Laplace transforms are used to define values for which functions converge absolutely.

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