# How do you find the asymptotes for #(12x^5 + 18x^2) /( 20x^4 + 9x^2)#?

Now performing the division

equating to cero

Solving for

then

so, for big

Note.

We don't have vertical assymptotes because

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To find the asymptotes of the rational function ( \frac{12x^5 + 18x^2}{20x^4 + 9x^2} ), we identify vertical asymptotes by determining where the denominator equals zero and any horizontal asymptotes by examining the behavior of the function as ( x ) approaches positive or negative infinity.

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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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