# How do you find the vertical, horizontal and slant asymptotes of: #f(x)=x/(x-1)^2#?

The vertical asymptote is

No slant asymptote.

The horizontal asymptote is

graph{x/(x-1)^2 [-10, 10, -5, 5]}

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To find the vertical asymptotes of the function (f(x) = \frac{x}{(x-1)^2}), we look for values of (x) that make the denominator zero but not the numerator. In this case, the vertical asymptote occurs at (x = 1).

To find the horizontal asymptote, we compare the degrees of the numerator and denominator. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is located at (y = 0).

To find the slant (oblique) asymptote, we divide the numerator by the denominator using polynomial long division. After performing the division, if the quotient is a polynomial function, it represents the slant asymptote. In this case, the quotient is (y = 1). Therefore, the slant asymptote is (y = x + 1).

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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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