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

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To find the limit of (2-x)/(x^2-4) as x approaches 2, we can substitute the value of 2 into the expression. However, this would result in division by zero, which is undefined.

To overcome this, we can factorize the denominator (x^2-4) as (x-2)(x+2).

Now, we can cancel out the common factor of (x-2) in the numerator and denominator.

After canceling, we are left with 1/(x+2).

Substituting x=2 into this expression, we get 1/(2+2) = 1/4.

Therefore, the limit of (2-x)/(x^2-4) as x approaches 2 is 1/4.

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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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