# How do you find the vertical, horizontal or slant asymptotes for #f(x) = (x^2 - 2x + 1)/(x)#?

Vertical asymptote is

No horizontal asymptote

Oblique asymptotes is

An ASYMPTOTE is a line that approches a curve, but NEVER meets it.

To find the vertical asymptote , put the denominator = 0 (because 0 cannot divide any number) and solve.

Here,

The curve will never touch the line

Next, we find the horizontal asymptote:

Compare the degree of the expressions in the numerator and the denominator.

Since,

There are

The oblique asymptote is a line of the form y = mx + c.

Oblique asymtote exists when the degree of numerator = degree of denominator + 1

To find the oblique asymptote divide the numerator by the denominator.

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To find the vertical asymptotes of ( f(x) = \frac{x^2 - 2x + 1}{x} ), identify the values of ( x ) for which the denominator equals zero. In this case, ( x = 0 ) is the only vertical asymptote.

To find the horizontal asymptote, compare the degrees of the numerator and denominator. Since the degree of the numerator (which is 2) is equal to the degree of the denominator (which is 1), there is no horizontal asymptote.

To find any slant asymptotes, perform polynomial long division of the numerator by the denominator. In this case, ( x ) divides into ( x^2 - 2x + 1 ) to yield ( x - 2 ), with no remainder. So, there is a slant asymptote at ( y = x - 2 ).

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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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