# How do you find the limit of # 1 / (x-2)^2# as x approaches 2?

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To find the limit of 1 / (x-2)^2 as x approaches 2, we can use algebraic manipulation.

First, we substitute 2 into the expression: 1 / (2-2)^2. This simplifies to 1 / 0^2, which is undefined.

However, we can use a different approach called factoring. By factoring the denominator, we can rewrite the expression as 1 / (x-2)(x-2).

Now, we can see that as x approaches 2, the denominator (x-2)(x-2) approaches 0.

To evaluate the limit, we can take the reciprocal of the denominator, giving us (x-2)(x-2) / 1.

Since the numerator (x-2)(x-2) approaches 0 as x approaches 2, the limit of 1 / (x-2)^2 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.

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