LimitsHard
Question
If f(x) = [x2] + 
, where [.] and {.} denote the greatest integer and fractional part functions respectively, then-
, where [.] and {.} denote the greatest integer and fractional part functions respectively, then- Options
A.f(x) is continuous at all integral points except 0
B.f(x) is continuous and differentiable at x = 0
C.f(x) is discontinuous for all x ∈ I − {1}
D.f(x) is not differentiable for all x ∈ I
Solution
f(x) =
⇒
(1 + 0) = 1∴
f(x) ⇒ 
(0 + 1) = 1and f(1) = 1 ⇒
f(x) = f(1) ∴ continuous at x = 1
similarly we check for another integers
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