Q6 of 48 Page 364

Show that ƒ(x) = [x] is neither continuous nor derivable at x=2.

Left hand limit at x = 2



Right hand limit at x = 2



As left hand limit ≠ right hand limit


Therefore, f(x) is not continuous at x = 2


Lets see the differentiability of f(x):


LHD at x = 2




RHD at x = 2




As, LHD ≠ RHD


Therefore,


f(x) is not derivable at x = 2


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