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 -...

## See

This Answer NowStart your **subscription** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

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.**