# How do you find the slant asymptote of # ( x^4 + 1 ) / ( x^2 + 2 )#?

This rational function is asymptotic to a parabola, not a line.

It has no slant asymptote.

As a result this rational function is asymptotic to a parabola, not a line.

More explicitly:

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To find the slant asymptote of the function ( \frac{x^4 + 1}{x^2 + 2} ), we need to perform polynomial long division to divide ( x^4 + 1 ) by ( x^2 + 2 ).

Dividing ( x^4 + 1 ) by ( x^2 + 2 ), we get:

( x^2 - 2x + 4 ) with a remainder of ( -7x + 9 ).

Therefore, the slant asymptote of the function is ( y = x^2 - 2x + 4 ).

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To find the slant asymptote of ( \frac{x^4 + 1}{x^2 + 2} ), perform polynomial long division. The quotient will be the equation of the slant asymptote.

( \frac{x^4 + 1}{x^2 + 2} = x^2 - 2 + \frac{5}{x^2 + 2} )

Therefore, the slant asymptote is ( y = x^2 - 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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