# How do you find #lim theta costheta# as #theta->oo#?

DNE

So:

And:

Maybe it's stating the obvious but because cosine is periodic, there is no limit.

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The limit of theta times cosine of theta as theta approaches infinity is undefined.

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To find ( \lim_{\theta \to \infty} \theta \cos(\theta) ), we can analyze the behavior of the function as ( \theta ) approaches infinity.

As ( \theta ) becomes very large, the oscillatory behavior of ( \cos(\theta) ) causes it to fluctuate between -1 and 1. Since ( \theta ) is also growing without bound, the product ( \theta \cdot \cos(\theta) ) does not approach a finite limit as ( \theta ) approaches infinity.

Therefore, the limit ( \lim_{\theta \to \infty} \theta \cos(\theta) ) does not exist in the traditional sense because the product ( \theta \cdot \cos(\theta) ) oscillates indefinitely as ( \theta ) increases without bound.

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