# How do you find the asymptotes for #f(x) = x / (3x(x-1))#?

Vertical:

Horizontal:

Vertical asymptotes:

Solved, this gives

Horizontal asymptotes:

graph{x/(3x(x-1)) [-10, 10, -5, 5]}

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To find the asymptotes for the function ( f(x) = \frac{x}{3x(x-1)} ), first check for vertical asymptotes by setting the denominator equal to zero and solving for ( x ). Next, check for horizontal asymptotes by comparing the degrees of the numerator and denominator. If the degrees are the same, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 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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