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Laplace transform, book example 
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#1
Apr1908, 03:56 PM

P: 436

I'm having trouble following one of the steps in my textbook. They give a function:
[tex] y(t) = e^{2t} [/tex] and plug it into [tex] Y(s) = \int_{0}^{\infty} y(t) e^{st} dt [/tex] and compute. They end up with: [tex] \frac{1}{2s} \underbrace{lim}_{b > \infty} e^{(2s)b}[/tex] (call this part 1) Which will converge to zero if s > 2. Then they state "we see that the improper integral for Y(s) does not converge if s is less than or equal to 2, and that [tex] Y(s) = \frac{1}{s2} [/tex] if s >2. " (call this part 2) I don't get how they got from part 1 to part 2. How does the denominator go from 2s to s2, and why does the exponential go away? Any help is appreciated. 


#2
Apr1908, 04:15 PM

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#3
Apr1908, 04:22 PM

P: 436

Oh ok, I see why they did that now. Thank you!



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