Lim cos x as x approaches infinity

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What is the limit as x approaches infinity of cosx?

If the highest power of the numerator is the same as the highest power of the denominator, then the limit of the expression as x x approaches infinity is the ratio of the
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Evaluate the Limit limit as x approaches infinity of (cos(x))/x

I have to prove that cos ( x) has no limit as x approaches infinity. Let ϵ > o and M be any number greater than 0, so that for any x>M: | cos ( x) − L | < ϵ. I'm not sure how am I to show that for a