# How do you find the limit of #sqrt(x^2-9)/(2x-6)# as #x->oo#?

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To find the limit of sqrt(x^2-9)/(2x-6) as x approaches infinity, we can simplify the expression by dividing both the numerator and denominator by x. This gives us sqrt(1-9/x^2)/(2-6/x). As x approaches infinity, 9/x^2 approaches 0 and 6/x approaches 0. Therefore, the expression simplifies to sqrt(1-0)/(2-0), which is equal to 1/2. Hence, the limit of sqrt(x^2-9)/(2x-6) as x approaches infinity is 1/2.

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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.

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