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Math Help - infinite limits on trigonometric functions

  1. #1
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    infinite limits on trigonometric functions

    Hi All,

    Could any one explain me how to solve this problem.

    what is the value of cos(px), if x tends to infinite.

    From the Dirac delta function, del(p) = limit(x tends to infinite) {sin(px)/(pi*p)}.

    here 'p' is a constant.

    Instead of using the relation between the sin and cos, Is there any other way to solve the above problem.


    another request : How to type mathematical expression in the threads?
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  2. #2
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    Quote Originally Posted by kurapati View Post
    Hi All,

    Could any one explain me how to solve this problem.

    what is the value of cos(px), if x tends to infinite.
    The definition of "limit as x goes to infinity" is: \lim_{x\rightarrow\infty} f(x)= L if and only if, given any \epsilon> 0 there exist X such that if x> X then |f(x)- L|< \epsilon. That is impossible for cos(px) because, no matter how large x is, there exist values of x ( x= n\pi for n an even integer) such that cos(x)= 1 and values of x ( x= n\pi for n an odd integer) such that cos(x)= -1. Since it keeps going from -1 to 1, it can't converge to a specific limit. The limit does not exist.

    From the Dirac delta function, del(p) = limit(x tends to infinite) {sin(px)/(pi*p)}.

    here 'p' is a constant.

    Instead of using the relation between the sin and cos, Is there any other way to solve the above problem.
    Solve what problem? As I said, limit of cos(px), as x goes to infinity, does not exist. If you are asking about that formula for the Dirac Delta function, the Dirac Delta Function is a "distribution" or "generalized function" , NOT a function. In any case, I don't see how that limit has anything to do with the delta function which can be described as "infinite if p= 0, 0 for all other values of p" which is not the case for that limit. Where did you get that formula?

    another request : How to type mathematical expression in the threads?
    Use "LaTex". On this board begin a mathematical expression with  and end with .
    Here is a good tutorial on LaTex:
    Getting to Grips with Latex - Mathematics - Latex Tutorials by Andrew Roberts @ School of Computing, University of Leeds

    Note that different boards may use different html tags to start and end LaTex. I have seen "" (here), "", and even "\( \)".
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