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February 17th, 2017, 02:18 AM   #1
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proving formula of Laplace

Hello everybody

I want to find how to proving formula of Laplace in pic no1 from the basic limit formula of pic no.2


Thank and best regards
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File Type: jpg no2.jpg (94.1 KB, 2 views)
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February 17th, 2017, 03:42 AM   #2
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All of them?

Could you pick one that you're finding particularly difficult maybe?
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February 17th, 2017, 04:16 AM   #3
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Start with an easy one i guess...

Let $\displaystyle f(t) = u(t) = $$\displaystyle

\left\{ \begin{array}{rl}
0, &\mbox{ t $\displaystyle <$ 0} \\
1, &\mbox{ t $\displaystyle \geq$ 0}
\end{array} \right.

$

Since we aren't concerned values of $\displaystyle t$ less than $\displaystyle 0$, we can allow $\displaystyle f(t) = 1$.

Then we simply need to compute the following, which ill leave you to do .

$\displaystyle \int_{0}^{\infty} e^{-s t} dt$
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February 17th, 2017, 10:44 AM   #4
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Quote:
Originally Posted by Joppy View Post
All of them?

Could you pick one that you're finding particularly difficult maybe?
Yes please, if you have any paper photo of all of solutions i'll will be grateful of you.

because i passed this in three yrs ago in college, and i forgotten the details.

best regards

Last edited by almahdi; February 17th, 2017 at 11:29 AM.
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February 19th, 2017, 11:09 PM   #5
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Quote:
Originally Posted by almahdi View Post
Yes please, if you have any paper photo of all of solutions i'll will be grateful of you.

because i passed this in three yrs ago in college, and i forgotten the details.

best regards
Yes but what details exactly? Trouble with integration or applying the definition of L.T. ?
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February 26th, 2017, 01:19 AM   #6
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I wrote a few of them up. Let me know if there are any mistakes.
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