# How do you use limits to find a horizontal asymptote?

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To use limits to find a horizontal asymptote, you need to evaluate the limit of a function as it approaches positive or negative infinity. If the limit is a finite number, then that number represents the horizontal asymptote. If the limit is positive or negative infinity, or if it does not exist, then there is no horizontal asymptote.

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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 # (sin^2(x^2))/(x^4)# as x approaches 0?
- How do you find the limit of #(sqrt(6-x)-2)/(sqrt(3-x) -1)# as x approaches 2?
- Evaluate #lim_(x rarr -oo) sqrt(x^2 + x) - x #?
- How do you find #lim sqrt(u^2-3u+2)-sqrt(u^2+1)# as #u->oo#?
- How do you evaluate # (3x^2 - x) /( 7x^2 - 10)# as x approaches infinity?

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