# How do I find the limit as x approaches infinity of a trigonometric function?

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#lim_(x->oo)(x^2csc3xtan6x)/(cos7xcot^2x)#

The limit does not exist...

First, think about:

There are periods for each of the component trigonometric functions:

Additionally, keep in mind that every trigonometric function is continuous across all of its domains.

Hence:

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To find the limit as ( x ) approaches infinity of a trigonometric function, consider the behavior of the function as ( x ) becomes increasingly large. Identify any periodic behavior and determine if the function approaches a finite value or oscillates indefinitely. If the function contains terms like sine or cosine, consider using trigonometric identities to simplify the expression before evaluating the limit. If the limit exists and is finite, that value is the limit as ( x ) approaches infinity. If the limit is infinite or oscillates indefinitely, state that the limit does not exist.

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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.

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