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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?


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Sounds like a homework problem. Please add a homework tag, and explain what your thoughts are. What have you tried? –  gt6989b Oct 31 '12 at 19:48
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? –  Beni Bogosel Oct 31 '12 at 20:16
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1 Answer 1

up vote 6 down vote accepted

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

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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 '13 at 1:56
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