` lim_ ( x to 2) (|x-2|)/(x-2) =`

Options

A. `0`
B. `1`
C. `-1`
D. अस्तित्व नहीं है

Answer

D

Explanation

` x gt 2, | x - 2| = ( x -2) `
` :. R.H.L = lim _( xto 2+0) f(x) = lim _( x to 2+0) (|x-2|)/(x-2)`
` = lim _ ( x to 2 + 0) (x-2)/( x-2) = 1 `
` L.H.L = lim _( x to 2 -0) f( x) = lim _ ( x to 2 -0) f(x) = lim _ ( x to 2 -0) (|x-2|)/(x-2)`
` = lim _( x to 2 - 0 ) (-(x-2))/(x-2) = -1`
` :. R.H.L !=L.H.L`
अतः ` lim _ ( x to 2) (|x-2|)/(x-2) ` का अस्तित्व नहीं है ।