# How do you find the slant asymptote of #y=(x^2+12)/(x-2)#?

The slant asymptote is

The slant asymptote occurs when the degree in the numerator is one greater than the degree in the denominator.

Since the denominator is a linear factor, you can use either long division or synthetic division to find the slant asymptote.

Subtract and bring down the next monomial in the dividend:

Multiply this monomial in the quotient by each monomial in the divisor, then subtract:

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To find the slant asymptote of the function ( y = \frac{x^2 + 12}{x - 2} ), you can perform polynomial long division to divide ( x^2 + 12 ) by ( x - 2 ). The slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator after division.

Perform the division as follows:

- Divide ( x^2 ) by ( x ) to get ( x ).
- Multiply ( x ) by ( x - 2 ) to get ( x^2 - 2x ).
- Subtract ( x^2 - 2x ) from ( x^2 + 12 ) to get ( 2x + 12 ).
- Divide ( 2x ) by ( x ) to get ( 2 ).
- Multiply ( 2 ) by ( x - 2 ) to get ( 2x - 4 ).
- Subtract ( 2x - 4 ) from ( 2x + 12 ) to get ( 16 ).

After performing the division, you get ( x + 2 + \frac{16}{x - 2} ). The slant asymptote is the linear term ( x + 2 ) in this expression. Therefore, the slant asymptote of the function ( y = \frac{x^2 + 12}{x - 2} ) is ( 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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