Lim as x approaches 2 from the right of |x-2|÷x-2

Question

Evaluate analytically

Answer 1

Do you mean

                                   |x-2|

lim (as x-->2⁺) -------------       ?

                                   (x-2)

 

IF so, the answer is 1.   That ratio abs(x-2)/(x-2) = 1 to the right of x=2, and it =-1 to the left of x=2.

 

Analytically, for x<2 |x-2| becomes -x+2   and the ratio becomes  (-x+2)/(x-2) = (-1)(x-2)/(x-2) = -1

 

For x>2,  |x-2| = x-2, and the ratio becomes (x-2)/(x-2) = 1