# How do you find the limit of #(x^2-3x+2)/(x^3-4x)# as x approaches 2?

Factorize the numerator and denominator:

As in this form the function is continuous, the limit equals the value:

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To find the limit of (x^2-3x+2)/(x^3-4x) as x approaches 2, we can substitute the value of 2 into the expression. This gives us (2^2-3(2)+2)/(2^3-4(2)). Simplifying further, we get (4-6+2)/(8-8), which equals 0/0. This is an indeterminate form. To evaluate the limit, we can use algebraic manipulation or L'Hôpital's rule. Applying L'Hôpital's rule by taking the derivative of the numerator and denominator separately, we get (2-3)/(3(2^2)-4) = -1/8. Therefore, the limit of (x^2-3x+2)/(x^3-4x) as x approaches 2 is -1/8.

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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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