Periodic functions confusiom

Loki123 said:
cos(ln(x+2pi)) i don't know how to turn that to cos(ln(x))
Click to expand...
Maybe it isn't possible! Has anyone said yet that you were basically right in the OP, and we're just trying to help you convince yourself?

Proving that a function is not periodic is a little harder than proving that it is! Rather than trying to make it work and failing forever, you need to try looking for a feature of the function that is incompatible with periodicity.

I gave a suggestion for that in post #13: if the zeros of the function are not equally spaced, then it can't be periodic.

When is cos(ln(x)) = 0?

(This is not the only way.)
 
Dr.Peterson said:
Maybe it isn't possible! Has anyone said yet that you were basically right in the OP, and we're just trying to help you convince yourself?

Proving that a function is not periodic is a little harder than proving that it is! Rather than trying to make it work and failing forever, you need to try looking for a feature of the function that is incompatible with periodicity.

I gave a suggestion for that in post #13: if the zeros of the function are not equally spaced, then it can't be periodic.

When is cos(ln(x)) = 0?

(This is not the only way.)
Click to expand...
lnx=Pi/2+kPi

x=e^(Pi/2+kPi)
 
Loki123 said:
so here is the thing, in my mind it makes sense that it's not periodic, but if someone were to ask me why, i could not formulate an answer.
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cos(ln(x)) is NOT periodic because the function value does not repeat with a "period".

There is a difference between periodic and oscillating function. Use Wolframalpha.com to confirm or discard.
 
Subhotosh Khan said:
cos(ln(x)) is NOT periodic because the function value does not repeat with a "period".

There is a difference between periodic and oscillating function. Use Wolframalpha.com to confirm or discard.
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I won't have Wolfram alpha on a test
 
Loki123 said:
I won't have Wolfram alpha on a test
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Wolframalpha.com is a short-cut to confirm your answer while doing HOMEWORK. If you need to, you can always do the same with PENCIL & PAPER and a bit of diligence.
 
Subhotosh Khan said:
Wolframalpha.com is a short-cut to confirm your answer while doing HOMEWORK. If you need to, you can always do the same with PENCIL & PAPER and a bit of diligence.
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but I don't know how to do it with pencil & paper and a bit of diligence. that's why i am here.
 
Actually you

don't WANT TO know how to DISCOVER it with pencil & paper and a bit of diligence. that's why YOU ARE here.

You want somebody to TELL you.
 
Subhotosh Khan said:
Actually you

don't WANT TO know how to DISCOVER it with pencil & paper and a bit of diligence. that's why YOU ARE here.

You want somebody to TELL you.
Click to expand...
no, i want to know it on my own, but i have a hard time figuring it out. not all of us have the same capacity for mathematics... If I wanted to know just the answer, i would use the wolfram alpha, circle the correct answer and be done with it. Don't assume things like that. ever.
 
I had enough of this post.
Here is what you need to know. If you can't understand what I am about to say, then you just don't have he ability, at least right now, to understand this problem.

cos(lnx). For this to be periodic, there must be some constant, c, such that ln(x) and ln(x+c) differ by 2pi for all x.
If they differ by 2pi, then ln(x+c) = ln(x) + 2pi and cos(ln(x+c)) = cos(lnx+2pi) and cos(lnx) would be periodic.

The question is can you find c?


Take any value for x, say 7. You want another x value, x*, such that ln7 and lnx* differ by 2pi.
That is solve lnx* - ln 7 =2pi.
Get ln(x*/7) = 2pi. The e^(2pi) = x*/7 and x* = 7e^(2pi).
Now c = x*-7 = 7(e^(2pi)-1).

Now pick another x value, say 9 or any value of your choice, and compute c. Are the two c values the same. If not, then cos(lnx) is not periodic.
 
Steven G said:
I had enough of this post.
Here is what you need to know. If you can't understand what I am about to say, then you just don't have he ability, at least right now, to understand this problem.

cos(lnx). For this to be periodic, there must be some constant, c, such that ln(x) and ln(x+c) differ by 2pi for all x.
If they differ by 2pi, then ln(x+c) = ln(x) + 2pi and cos(ln(x+c)) = cos(lnx+2pi) and cos(lnx) would be periodic.

The question is can you find c?


Take any value for x, say 7. You want another x value, x*, such that ln7 and lnx* differ by 2pi.
That is solve lnx* - ln 7 =2pi.
Get ln(x*/7) = 2pi. The e^(2pi) = x*/7 and x* = 7e^(2pi).
Now c = x*-7 = 7(e^(2pi)-1).

Now pick another x value, say 9 or any value of your choice, and compute c. Are the two c values the same. If not, then cos(lnx) is not periodic.
Click to expand...
now i get it! thanks!
 
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