# Thread: infinite limits on trigonometric functions

1. ## 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?

2. Originally Posted by kurapati
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: $\displaystyle \lim_{x\rightarrow\infty} f(x)= L$ if and only if, given any $\displaystyle \epsilon> 0$ there exist X such that if x> X then $\displaystyle |f(x)- L|< \epsilon$. That is impossible for cos(px) because, no matter how large x is, there exist values of x ($\displaystyle x= n\pi$ for n an even integer) such that cos(x)= 1 and values of x ($\displaystyle x= n\pi$ 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 $\displaystyle and end with$.
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 "".