# How do you find vertical, horizontal and oblique asymptotes for #y=1/(2-x)#?

Vertical asymptote

Horizontal asymptote

Mathematically you are not allowed to divide by 0. This situation is called 'undefined'.

So at

Suppose

As

In the same way, when

'

So

'...................................................................

When writing limits; when approaching a value from the positive side then for the value 2 it would be written as

Same way for approaching from the negative side it is

Thus

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Vertical asymptotes occur where the denominator of the rational function equals zero, so set (2 - x = 0) and solve for (x). For horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at (y = 0). If the degrees are equal, divide the leading coefficients of both terms to find the horizontal asymptote. If the degree of the numerator is greater, there's no horizontal asymptote. For oblique asymptotes, if the degree of the numerator is exactly one greater than the degree of the denominator, perform polynomial long division to find the equation of the oblique asymptote. Otherwise, there is no oblique asymptote.

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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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