How do you find #lim theta costheta# as #theta->oo#?
Paisley JohnsonDNE
So:
And:
Maybe it's stating the obvious but because cosine is periodic, there is no limit.
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Isabella AckermanThe limit of theta times cosine of theta as theta approaches infinity is undefined.
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Scarlett AllisonTo 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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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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