How do you find all the asymptotes for #(2x^3+11x^2+5x1)/(x^2+6x+5 )#?
First of all, we'll have a look on how to find asymptotes in general:
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To find the asymptotes of the given rational function, you first need to determine whether there are any vertical, horizontal, or slant asymptotes.

Vertical asymptotes occur where the denominator equals zero but the numerator does not. So, set the denominator equal to zero and solve for x. Any values of x that make the denominator zero but not the numerator will result in vertical asymptotes.

Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. If the degree of the numerator is greater, there is no horizontal asymptote. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients.

Slant asymptotes occur when the degree of the numerator is exactly one greater than the degree of the denominator. To find the slant asymptote, perform polynomial long division or use another appropriate method to divide the numerator by the denominator. The quotient obtained will be the equation of the slant asymptote.
Once you have determined the type of asymptotes, you can find their equations and graph the function accordingly.
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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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