(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Laplace transform, book example

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}{2-s} \underbrace{lim}_{b -> \infty} e^{(2-s)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}{s-2} [/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 2-s to s-2, and why does the exponential go away?

Any help is appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Laplace transform, book example

**Physics Forums | Science Articles, Homework Help, Discussion**