Highly selective Backlog Qs for JEE MainMathematicsLimits

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

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