How solve Cosine with limit

Question

what is the result of

$$\lim_{T\to\infty} \frac{\cos (xT)}{T}$$

I don't know how to solve it. Can any one show me a simple way?

Regards

Sounds like a homework problem. Please add a homework tag, and explain what your thoughts are. What have you tried?
Intuitively, what happens if you divide something small by something big? After all, that's what the limit procedure says: when we make $T$ very great the ratio $\cos(xT)/T$ approaches which real number?

Babak S. · Accepted Answer · 2012-10-31 19:52:52Z

up vote 7 down vote accepted

Hint: Use the Squeeze theorem and note that $|\cos(x)|\leq1$ if your limit is like $$\lim_{x\to\infty} \frac{1}{x}\cos(ax)$$

answered Oct 31 '12 at 19:52

Babak S.
27.9k21249

	But the OP used $x$ instead of $a$! – Basil R Nov 1 '12 at 7:39
	Nice hint! It "did the job", and well! – amWhy Apr 2 at 1:56

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