# How do you find the asymptotes for #f(x) = (5x)/(x^2-1)#?

vertical asymptotes at x = ± 1

horizontal asymptote at y = 0

Vertical asymptotes occur as the denominator of a rational function tends to zero.To find the equation, let the denominator equal zero.

If the degree of the numerator is less than the degree of the denominator, as is the case here, numerator degree 1 , denominator degree 2.

Then the equation is y = 0

Here is the graph as an illustration of the asymptotes. graph{5x/(x^2-1) [-10, 10, -5, 5]}

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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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