# How do you find the asymptotes for # s(t)=(8t)/sin(t)#?

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To understand the approaches fpr limits and limits better, recall that sine is positive in the first two quadrants and negative in the third and fourth.

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To find the asymptotes of the function ( s(t) = \frac{8t}{\sin(t)} ), identify where the function is undefined and where it approaches infinity. Asymptotes occur where the function approaches infinity or is undefined.

The function is undefined where the denominator, ( \sin(t) ), equals zero. This happens when ( t = n\pi ), where ( n ) is an integer. Therefore, the vertical asymptotes occur at ( t = n\pi ).

Additionally, to find the horizontal asymptotes, examine the behavior of the function as ( t ) approaches positive or negative infinity. As ( t ) approaches infinity, ( \sin(t) ) oscillates between -1 and 1, so the function ( s(t) ) approaches positive or negative infinity, depending on the sign of ( t ). Therefore, there are no horizontal asymptotes for this function.

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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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