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

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To find the limit of (sqrt(x) - sqrt(2))/sqrt(x^2 - 2x) as x approaches 2, we can simplify the expression by rationalizing the numerator. By multiplying both the numerator and denominator by the conjugate of the numerator, which is (sqrt(x) + sqrt(2)), we can eliminate the square root in the numerator. After simplifying, we get (x - 2)/(sqrt(x^2 - 2x) * (sqrt(x) + sqrt(2))).

Next, we can factor out (x - 2) from the numerator and rewrite the denominator as sqrt(x(x - 2)) * (sqrt(x) + sqrt(2)).

Now, we can cancel out the common factor of (x - 2) in the numerator and denominator.

After canceling, we are left with 1/(sqrt(x) + sqrt(2)).

Finally, as x approaches 2, the denominator approaches sqrt(2) + sqrt(2) = 2sqrt(2).

Therefore, the limit of (sqrt(x) - sqrt(2))/sqrt(x^2 - 2x) as x approaches 2 is 1/(2sqrt(2)).

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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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