# How do you find #lim (x-1)/(x-2sqrtx+1)# as #x->1^+#?

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To find the limit of (x-1)/(x-2sqrt(x)+1) as x approaches 1 from the positive side, we can substitute the value of x into the expression. Doing so, we get (1-1)/(1-2sqrt(1)+1), which simplifies to 0/0. This is an indeterminate form. To evaluate this limit, we can use L'Hôpital's rule. Taking the derivative of the numerator and denominator separately, we get (1)/(1/2sqrt(x)). Substituting x=1 into this derivative, we get 1/(1/2sqrt(1)), which simplifies to 1/1/2, or 2. Therefore, the limit of (x-1)/(x-2sqrt(x)+1) as x approaches 1 from the positive side is 2.

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