AP EAMCET202123 Aug 2021Morning ShiftMathematicsLimitsActual
The limit _ x 1 1- 2(x-1) x-1
Options
- Aexists and is equal to 2
- Bexists and is equal to - 2
- Cdoes not exist
- Dexists and is equal to ( 1 2 )
Correct answer
C. does not exist
Step-by-step solution
Let array rlr L & = _ x 1 1- 2(x-1) x-1 & & = _ x 1 2 ^2(x-1) x-1 [ 1- 2 =2 ^2 ] & = 2 _ x 1 | (x-1)| x-1 & [ 0 0 . form ] & = 2 _ (x-1) 0 | (x-1)| x-1 & & = 2 _ z 0 | z| z & [Let x-1=z] array [Let x-1=z ] aligned & NHL = 2 _ z 0⁺ z z = 2 & LHL = 2 _ z 0⁻ - z z =- 2 aligned RHL LH Limit does not exist.