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

can be made as large as we want and is always positive.

Then:

and so:

and:

which proves the limit.

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To determine the limit of 1/(x-2)^2 as x approaches 2, we can use algebraic manipulation. By substituting x=2 into the expression, we get 1/(2-2)^2, which simplifies to 1/0. Since division by zero is undefined, we cannot directly evaluate the limit using substitution. However, we can use a different approach called factoring. By factoring the denominator, we can rewrite the expression as 1/[(x-2)(x-2)]. Canceling out the common factors, we are left with 1/(x-2). Now, substituting x=2 into this expression, we get 1/(2-2), which simplifies to 1/0. Again, division by zero is undefined. Therefore, the limit of 1/(x-2)^2 as x approaches 2 does not exist.

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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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