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## ASYMPTOTE

Hello,

Please see the attached MC 15 worksheet.

I need help in finding:

1- Maximum values of Q1(x), Q2(x) and Q3(x)

2- Asymptote to y(x), z(x) and Z(x) (How can we verify that these curves have horizontal ASYMPTOTES?)

Thank you so much.

Anousheh

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1 ACCEPTED SOLUTION

Accepted Solutions

## Re: ASYMPTOTE

ad 1) you could use root and the derivative, as odesolve returns sort of a pseudo-functions (vector of points but implicit interpolation) from which you can take the derivative and use root on it. See attached.

ad 2) you can't. The "functions" you have are only valid for 400<=x<=1000, so you can't explore what happens if x approaches infinity (which would be necessary to prove that a horizontal asymptote exists). The best you can "prove" is that all available values Z(x) are smaller than Z(1000) - thats no prove for a limit of course.

To verify a horizontal asymptote you would need Z(x) in an analytical form, that means you will have to solve the DE manually or with the help of Laplace, if possible. Then you could take the limit x-->inf and see what happens.

7 REPLIES 7

## Re: ASYMPTOTE

ad 1) you could use root and the derivative, as odesolve returns sort of a pseudo-functions (vector of points but implicit interpolation) from which you can take the derivative and use root on it. See attached.

ad 2) you can't. The "functions" you have are only valid for 400<=x<=1000, so you can't explore what happens if x approaches infinity (which would be necessary to prove that a horizontal asymptote exists). The best you can "prove" is that all available values Z(x) are smaller than Z(1000) - thats no prove for a limit of course.

To verify a horizontal asymptote you would need Z(x) in an analytical form, that means you will have to solve the DE manually or with the help of Laplace, if possible. Then you could take the limit x-->inf and see what happens.

## Re: ASYMPTOTE

Valery, do you really think thats of any help here?

## Re: ASYMPTOTE

Hello Werner,

Thank you so much for the input. Very helpful.

All the best,

Anousheh

## Re: ASYMPTOTE

Hello Valery,

Thanks for the information. I am trying to see if my functions, y(x) have any horizontal asymptote.

Werner correctly pointed out that:

The "functions" you have are only valid for 400<=x<=1000, so you can't explore what happens if x approaches infinity (which would be necessary to prove that a horizontal asymptote exists). The best you can "prove" is that all available values Z(x) are smaller than Z(1000) - thats no prove for a limit of course.

To verify a horizontal asymptote you would need Z(x) in an analytical form, that means you will have to solve the DE manually or with the help of Laplace, if possible. Then you could take the limit x-->inf and see what happens.

Nevertheless, your information is really good for constructing other type of asymptotes. Thank you.

Anousheh

## Re: ASYMPTOTE

 Werner Exinger wrote:Valery, do you really think thats of any help here?

Werner, do you really think thats of any help here?

## Re: ASYMPTOTE

 Valery Ochkov wrote:Werner Exinger wrote:Valery, do you really think thats of any help here?Werner, do you really think thats of any help here?

I'm not sure. If it helps avoiding inappropriate posting in the future, the answer is yes, if not - no.

No offence intended, but its sometimes really hard to follow a thread if its cluttered with "side postings" not related to the question other than it seemed to was triggered only by the mention of a single term ("asymptote" in this case). No hard feelings, anyway.

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