How do you find the asymptotes for #(x+3)/(x^29)#?
To find the asymptotes, you need to find out where the denominator approaches zero for the vertical asymptotes and then establish what happens as
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To find the asymptotes of the rational function ( \frac{x + 3}{x^2  9} ), follow these steps:

Identify any vertical asymptotes by determining where the denominator equals zero. In this case, ( x^2  9 = 0 ), which yields ( x = 3 ) and ( x = 3 ) as vertical asymptotes.

Determine any horizontal asymptotes by examining the behavior of the function as ( x ) approaches positive or negative infinity. If the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at ( y = 0 ). If the degree of the numerator equals the degree of the denominator, the horizontal asymptote is given by the ratio of the leading coefficients. In this case, since the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at ( y = 0 ).
Therefore, the vertical asymptotes are ( x = 3 ) and ( x = 3 ), and the horizontal asymptote is ( y = 0 ).
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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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