Hello, Everyone. Thanks in advance for your time and help. Best Regards.

Where is your problem? You simply let Mathcad do its job without any tricks at all:A better way with a little thinking over the problem beforehand may be this:

L

lvl107

20-Turquoise

Solved

atan( ) , ln( ) and Find( ) _ (2)

Forum|Forum|12 years ago
February 10, 2014
5 replies
8625 views

Hello, Everyone.

atan%28+%29+%2C+ln%28+%29++and+Find%28+%29+_+%282%29.PNG

Thanks in advance for your time and help.

Best Regards.

1_atan(-)-,-ln(-)-and-Find(-)-_-(2)-xmcd.zip

Other

Best answer by Werner_E

Where is your problem? You simply let Mathcad do its job without any tricks at all:

16.02a.png

A better way with a little thinking over the problem beforehand may be this:

16.02b.png

R

RichardJ

19-Tanzanite

I'm not sure what you are looking for. The symbolic solution for X is just tan(LHS). Or are tthe x on the LHS and the X on the RHS supposed to be the same?

R

RichardJ

19-Tanzanite

Hmmm. Actually, Given...Find gives an interesting answer. What is "ImageSet"?

1_atan(-)-,-ln(-)-and-Find(-)-_-(2)-xmcdz.zip

L

lvl107

Author

20-Turquoise

Thanks for your time and help, Richard. And I have a query :

Best Regards.

1_atan(-)-,-ln(-)-and-Find(-)-_-(2')-xmcd.zip

L

lvl107

Author

20-Turquoise

And need help with the related query :

%283%29.PNG

Thanks in advance for your time and help.

Best Regards.

1_atan(-)-,-ln(-)-and-Find(-)-_-(2'')-xmcd.zip

W

Werner_E

25-Diamond I

You probably expect X=i, but again you have to consider the ambiguity of the used function(s):

10.02.png

Different results for X depending on the value of x!

L

lvl107

Author

20-Turquoise

And I have another related query :

Thanks in advance for your time and help.

Best Regards.

1_Definite-Integral--xmcd.zip

W

Werner_E

25-Diamond I

You may either evaluate the integral numerically or symbolically with the modifier "float".

L

lvl107

Author

20-Turquoise

And I have another related question :

Thanks in advance for your time and help.

Best Regards.

1_ln(-)-and-atan(-)-xmcd.zip

W

Werner_E

25-Diamond I

You experience the effect of numerical inaccuracy combined with ambiguity of "functions" (again!). E.g. Mathcad choses pi for the atan(..) for some values of x, giving the total result -2pi. Mathcads numerics add the very small imaginary part (which should be zero) and so that point isn't plotted. This happens quite often and so you see the holes in your graph. Reformulating the function definition as I had shown in another thread with the f1b() may help, but mustn't necessary. If you want to be on the safe side, define f2(x):=0. 😉

Can you tell us what you want to achieve with all this? You seem to know that used function are equivalent and the difference should simplify to zero - at least given some implicit assumptions about the domain of the involved variables and functions which Mathcad doesn't make. So whats the goal of all these attempts?

I am not sure why MC can write atan() as ln() but not the other way round. Both functions show ambiguity if applied to complex arguments (so strictly spoken they can't be called function therefore). Maybe is has to do with the fact that ln() is unique in the domain real and so Mathcad refuses to rewrite it with an ambiguous atan(). Maybe is just one of the many disabilities of MCs symbolics. Maybe it even can be done using the right combination and order of symbolic assumptons and keywords, Maybe ....

L

lvl107

Author

20-Turquoise

Many thanks for the following, Werner :

Werner Exinger wrote:
You experience the effect of numerical inaccuracy combined with ambiguity of "functions" (again!). E.g. Mathcad choses pi for the atan(..) for some values of x, giving the total result -2pi. Mathcads numerics add the very small imaginary part (which should be zero) and so that point isn't plotted. This happens quite often and so you see the holes in your graph. Reformulating the function definition as I had shown in another thread with the f1b() may help, ...
I am not sure why MC can write atan() as ln() but not the other way round. Both functions show ambiguity if applied to complex arguments (so strictly spoken they can't be called function therefore). Maybe is has to do with the fact that ln() is unique in the domain real and so Mathcad refuses to rewrite it with an ambiguous atan(). Maybe is just one of the many disabilities of MCs symbolics. Maybe it even can be done using the right combination and order of symbolic assumptons and keywords, Maybe ....