How do you find the asymptotes for #(x4)/(x^23x4)#?
You start by factoring the denominator, which can be written as
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To find the asymptotes of ( \frac{x  4}{x^2  3x  4} ):

Determine if there are any vertical asymptotes by finding the values of ( x ) that make the denominator equal to zero. Solve the equation ( x^2  3x  4 = 0 ) to find these values.

If there are any horizontal asymptotes, determine them by analyzing the degree 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 the numerator and denominator to find the horizontal asymptote.

If the degree of the numerator is greater than the degree of the denominator, there are slant asymptotes. Find the slant asymptotes by performing polynomial long division or synthetic division to divide the numerator by the denominator. The quotient obtained represents the equation of the slant asymptote.

Once you've found any vertical, horizontal, or slant asymptotes, those are the asymptotes for the function.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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