# How do you find the limit of #f(x) = (x^2 + x - 6) / (x + 3) # as x approaches 2?

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To find the limit of f(x) = (x^2 + x - 6) / (x + 3) as x approaches 2, we can substitute the value of 2 into the function and simplify the expression. By doing this, we get (2^2 + 2 - 6) / (2 + 3) = (4 + 2 - 6) / 5 = 0/5 = 0. Therefore, the limit of f(x) as x approaches 2 is 0.

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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.

- What is the limit of #(sqrt x) / (x + 4)# as x approaches infinity?
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- How do you find the limit of #(e^-x-e^(-x/2))/sqrt(e^x+1)# as #x->oo#?
- How do you find the limit of #(x^2 - 8) / (8x-16)# as x approaches #sqrt8^+#?

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