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

Rewrite the expression using

First we write

Now, note that

Putting these together, we get

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To find the limit of (2-x)/(sqrt(4-4x+x^2)) as x approaches 2^+, we can substitute the value of x into the expression.

When x approaches 2^+, the expression becomes (2-2)/(sqrt(4-4(2)+(2^2))), which simplifies to 0/(sqrt(4-8+4)).

Further simplifying, we have 0/(sqrt(0)), which is equal to 0.

Therefore, the limit of (2-x)/(sqrt(4-4x+x^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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- What is the limit of #f(x)# as #x# approaches 0?

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