# What are the asymptotes of #f(x)=(x^2+1)/(x^2-9)#?

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

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The asymptotes of f(x)=(x^2+1)/(x^2-9) are vertical asymptotes at x = 3 and x = -3, and there are no horizontal asymptotes.

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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.

- How do you find the limit of #x/sqrt(9-x^2)# as x approaches -3+?
- How do you find the limit of #sqrt(x^2-9)/(2x-6)# as x approaches #-oo#?
- How do you find the Limit of #2x+5# as #x->-3# and then use the epsilon delta definition to prove that the limit is L?
- Find limits as x approaches positive and negative infinity of function f(x)= 4x^3 -x^4 ?
- How do you find any asymptotes of #f(x)=(x+3)/(x^2-4)#?

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