Find the limit of function f(x) given by f(x)=ln(x-1)/(x-2), x->2?

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We have to find the value of lim x-->2 [ ln (x - 1)/(x - 2)]

substituting x = 2, we get the indeterminate form 0/0; that permits the use of l'Hopital's Theorem and we can substitute the numerator and denominator with their derivatives

=> lim x-->2 [ (1/(x - 1))/1]

substitute x = 2

=> 1/(2 - 1)

=> 1

The required value of lim x-->2 [ ln (x - 1)/(x - 2)] = 1.

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