LimitsHard
Question
(1 - x + [x - 1] + [1 - x]) is equal to (where [.] denotes greatest integer function)Options
A.0
B.1
C.-1
D.does not exist
Solution
(1 - x + [x - 1] + [1 - x]) L.H.L.=
(1 - x + [x - 1] + [1 - x])=
(1 - (1 - h) + [1 - h - 1] + [1 - 1 + h])=
(h + [-h] + [h])= 0 - 1 + 0 = - 1
R.H.L.=
(1 - x + [x - 1] + [1 - x])=
(1 - (1 + h) + [1 + h - 1] + [1 - (1 + h)]=
(- h + [h] + [-h])= 0 + 0 - 1 = - 1
L.H.L. = R.H.L. = - 1
So
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