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

graph{1/(x-2)^2 [-16.35, 15.68, -5.32, 10.69]}

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

First, we substitute the value of x into the expression: 1 / (2 - 2)^2.

Since any number divided by zero is undefined, we cannot directly substitute x = 2 into the expression.

However, we can simplify the expression by factoring the denominator: (x - 2)^2 = (x - 2)(x - 2).

Canceling out the common factor of (x - 2), we are left with 1 / (x - 2).

Now, we can substitute x = 2 into this simplified expression: 1 / (2 - 2) = 1 / 0.

Again, any number divided 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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