How do you find the vertical, horizontal and slant asymptotes of: #f(x)= (4x^2+ 4x-24)/(x^4- 2x^3 - 9x^2+ 18x)#?
The numerator factors like this:
The denominator factors like this:
graph{(4x^2+4x-24)/(x^4-2x^3-9x^2+18x) [-10, 10, -5, 5]}
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To find the vertical asymptotes, set the denominator equal to zero 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 ( y = 0 ). If the degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote. If the degree of the numerator is greater, there is no horizontal asymptote. To find slant asymptotes, perform polynomial long division and the slant asymptote is the quotient.
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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.
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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