# What are the asymptote(s) and hole(s), if any, of # f(x) =x/(x^4-x^2)#?

It has horizontal asymptote

It has no slant asymptotes or holes.

Given:

graph{x/(x^4-x^2) [-10, 10, -5, 5]}

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The function f(x) = x/(x^4-x^2) has two vertical asymptotes at x = -1 and x = 1. There are no horizontal asymptotes. There is a hole at x = 0.

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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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