Continuity and DifferentiabilityHard

Question

Consider f(x) = 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

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