Continuity and DifferentiabilityMedium
Question
Consider f(x) = 
where [*] & {*} are the greatest integer function & fractional part function respectively, then -
where [*] & {*} are the greatest integer function & fractional part function respectively, then -Options
A.f(0) = ln2 ⇒ f is continuous at x = 0
B.f(0) = 2 ⇒ f is continuous at x = 0
C.f(0) = e2 ⇒ f is continuous at x = 0
D.f has an irremovable discontinuity at x = 0
Solution
LHL = 
(0 - h) [0 - h]2 log(1 + 0 - h)2
=
= ln2
RHL =
∴ RHL ≠ RHL
(0 - h) [0 - h]2 log(1 + 0 - h)2=
= ln2RHL =
∴ RHL ≠ RHL
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