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#1 2015-02-23 12:42:16
How do I show that this function is a constant?
How do I show that g(x) = cos(tan(sin ..... cos(tan(sin(x)))) .... ) ) is a constant?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2015-02-23 20:53:50
- Bob
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- Registered: 2010-06-20
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Re: How do I show that this function is a constant?
hi Agnishom,
I am unclear about what the 'pattern' of this function is. What goes in the ....s space.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2015-02-23 21:57:42
Re: How do I show that this function is a constant?
It is an infinite composition of cos tan sin
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2015-02-23 23:00:35
- Bob
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Re: How do I show that this function is a constant?
So do you mean:
or maybe
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#5 2015-02-23 23:35:52
- Olinguito
- Member
- Registered: 2014-08-12
- Posts: 649
Re: How do I show that this function is a constant?
I think it's like. this. Let
[list=*]
[*]
[/list]And . The problem is to show that is independent of the choice of x, right?
Bassaricyon neblina
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#6 2015-02-24 00:21:22
Re: How do I show that this function is a constant?
Yes.
This shows that the constant is around 0.7169229431689353
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#7 2015-02-24 09:29:23
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: How do I show that this function is a constant?
Much cleaner is:
g[x_] := Cos[Tan[Sin[x]]]N[Nest[g, x, 400] /. x -> 1, 20]0.71692294316893535645
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2015-02-24 12:40:18
Re: How do I show that this function is a constant?
Okay, but I did not ask to find the value
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#9 2015-02-24 14:14:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: How do I show that this function is a constant?
Might have led to an analytical idea.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2015-02-24 20:42:14
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: How do I show that this function is a constant?
I get that value too. You might be able to put together an analytic proof of existence like this.
Let y = cos(tan(sin(x))).
Establish the following properties:
(1) y is an even function.
(2) y = 1 when x = 0
(3) y is periodic.
(4) y > 0 for all x.
(5) There exists an x = k so that y is symmetrical in that line. (There are many but find the lowest > 0 )
(6) y is decreasing between x = 0 and x = k
(7) The line y = x cuts the curve once between x = 0 and x = k
(8) This intersection gives the value of the constant. The other properties should be sufficient to show it is unique.
Hint: Use the MIF function grapher to see what the graph of y looks like.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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