Continuity and DifferentiabilityHard
Question
Given f(x) = 
where { } & [ ] denotes the fractional part and the integral part functions respectively, then which of the following statement does not hold good -
where { } & [ ] denotes the fractional part and the integral part functions respectively, then which of the following statement does not hold good -Options
A.f (0-) = 0
B.f (0+) = 3
C.f(0) = 0 ⇒ continuity of f at x = 0
D.irremovable discontinuity of f at x = 0
Solution
RHL = 
= 3-[cot-1(-∞)] = 3 - 3 = 0
LHL =
{(0 - h)2} cos 
=
(0 - h)2 cos (e- ∞) = 0
= 3-[cot-1(-∞)] = 3 - 3 = 0
LHL =
{(0 - h)2} cos =
(0 - h)2 cos (e- ∞) = 0Create a free account to view solution
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