MHT CET202311 May 2023Morning ShiftMathematicsLimitsActual
The left-hand derivative of f (x)=[x] ( x) , at x= k , k is an integer and [ ] is the greatest integer function, is
Options
- A(-1)^ k ( k -1)
- B(-1)^ k -1 ( k -1)
- C(-1)^ k k
- D(-1)^ k -1 k
Correct answer
A. (-1)^ k ( k -1)
Step-by-step solution
aligned f(x)= & [x] ( x) LHD & = _ h 0 f(k-h)-f(k) -h & = _ h 0 [k-h] (k-h)-[k] k -h & = _ h 0 (k-1) (k - h)-k k -h & = _ h 0 (-1)^ k+1 (k-1) -0 -h [ k I] & =(-1)^k(k-1) aligned