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-224.79696475168280874 and meaning ?

lvl107
20-Turquoise

-224.79696475168280874 and meaning ?

Hello Everyone.

From :

II.PNG

Thanks in advance.

Regards.

13 REPLIES 13
Fred_Kohlhepp
23-Emerald I
(To:lvl107)

I'm curious!

 

Do these functions have actual applications?  Or are we just playing?

 

Mathcad is saying that your equation has a root (E(x) =0) at the number given (-221.____)

 

E-x.png

LucMeekes
23-Emerald III
(To:lvl107)

As demonstrated in the other thread (https://community.ptc.com/t5/PTC-Mathcad/solve-x-fully/td-p/578709) the two first terms ( e^x and -(1/e^(i*x))^i ) cancel out. You're left with (e^pi)*cot(x).

That should give repeated roots at pi/2 +n*pi.

 

Success!
Luc

Werner_E
25-Diamond I
(To:LucMeekes)

@LucMeekes

> the two first terms ( e^x and -(1/e^(i*x))^i ) cancel out.

No! Not if we see it as a complex calculation which we have to do as the imaginary unit "i" is involved.

LucMeekes
23-Emerald III
(To:Werner_E)

I see. Thanks for reminding me that (a^b)^c=a^(b*c) only when b and c are real numbers. When either one is complex, things become more complex.

 

Luc

lvl107
20-Turquoise
(To:LucMeekes)

Luc, I guess : "You mean that :"

 

If so, I agreed with you.

Best RegardsII.PNG

Werner_E
25-Diamond I
(To:lvl107)

This would only be true for one of the infinite number of curves of the family described above, namely the one with k=0:

B.png

For all the others muPad is not able to find exact solutions and so will only present one numeric value - and sometimes even a wrong one (or at least we reach the end of the numeric precision of the symbolics here):

B2.png

To be fair it must be said that we get a better result when we add "float,250" to the last eval, too (we get -2.3*10^-105 which is close enough to zero).

And while muPad is not respecting an assume statement the way we want in that case, its interesting that it still reacts (in a weird way) to assume statements:

B3.png

 

 

BTW, uncle Wolfram also has his troubles with expressions like these. Or does anybody think that Wolfram is correct with this:

B4.png

x=1.1 IS a correct solution but I would have expected Wolfram telling me that any number is solution like here:

B5.png

lvl107
20-Turquoise
(To:Werner_E)

Many thanks for help. 

III.PNG(Be cool down with somethings is different with ours.). (I guess I'm not sure above all) :

Best Regards.

Werner_E
25-Diamond I
(To:lvl107)

It's about time that you finally realize that Mathcad / muPad is simply not capable of delivering ALL solutions to more complicated equations that are not analytically solvable!

If you insist in getting all solution you will probably have to resort to a different, more capable program with better symbolics.

B.png

lvl107
20-Turquoise
(To:Werner_E)

I guess I just wish learning :

 

IV.PNG

The solution are given, I guess that only are solution of ;4.PNG  

V.PNG

I guess discussing is discussing about difference.

Best Regards.

lvl107
20-Turquoise
(To:lvl107)

Oh, no !Smiley Sad Now I realize I was wrong with the below. My guessing is not correct ! :

1-.PNG1a.PNG

So far, to solve it, I have to solve it "by hand" with root function and guess value. And I still have a query : "Is there a anyway else ? ( as writting a program function to get output at least two solutions at once ) 

   Best Regards.

       Loi.

Werner_E
25-Diamond I
(To:lvl107)

Keep in mind that with E(x) you are not just defining one single curve but rather a family E(x,k) of an infinite number of curves. One of them (k=36) has one root at the given -224,79..

For more details see here: https://community.ptc.com/t5/PTC-Mathcad/solve-x-fully/m-p/578762/highlight/true#M183096

Whenever the symbolics switches to float mode its not capable to give you all roots any more. Similar to numerical solve methods but with the difference that the numerics will respect any guess values or ranges ("root" function) while the symbolics usually will ignore any assume statement in this case.

B.png

-MFra-
21-Topaz II
(To:lvl107)

Hi liv107,

you could have fun reading this "novel" so you will take away many doubts and expand your maths knowledge ...... even if I am sure that you already know tthese topics ....

complex analysis.jpg

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