# How do you find the Vertical, Horizontal, and Oblique Asymptote given #s(t) = t / sin t#?

Vertical asymptotes where

graph{x/sinx [-46.2, 46.33, -23.06, 23.16]}

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To find the vertical asymptotes of ( s(t) = \frac{t}{\sin(t)} ), identify the values of ( t ) where the denominator (( \sin(t) )) equals zero. These values will result in vertical asymptotes.

The horizontal asymptote can be found by analyzing the behavior of the function as ( t ) approaches positive or negative infinity.

To find oblique asymptotes, perform polynomial long division to divide the numerator (( t )) by the denominator (( \sin(t) )). The quotient obtained from this division represents the equation of the oblique asymptote.

In summary:

- Vertical asymptotes occur where ( \sin(t) = 0 ).
- The horizontal asymptote can be determined by analyzing the limit of the function as ( t ) approaches positive or negative infinity.
- Oblique asymptotes can be found through polynomial long division of the numerator by the denominator.

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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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