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

graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}

The numerator is the difference of two squares, and as such we can factorise using it as

Se we can factorise as follows:

Which is completely consistent with the above graph.

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To find the limit of (x^2-4)/(x-2) as x approaches 2, we can simplify the expression by factoring the numerator. (x^2-4) can be factored as (x-2)(x+2). Canceling out the common factor of (x-2) in the numerator and denominator, we are left with (x+2). Substituting x=2 into (x+2), we get 2+2=4. Therefore, the limit of (x^2-4)/(x-2) as x approaches 2 is 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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