Continuity and DifferentiabilityHard
Question
The left hand derivative of f(x) = [x] sin (π x) at x = k, k is an integer, is
Options
A.(-1)k (k - 1)π
B.(-1)k-1 (k - 1)π
C.(-1)k kπ
D.(-1)k-1 kπ
Solution
Given f(x) = [x] sin π x
If x is just less than k,[x] = k - 1
∴ f(x) = (k -1) sin π x
LHD of f(x)
where x = k - h
= (-1)k (k - 1)π
If x is just less than k,[x] = k - 1
∴ f(x) = (k -1) sin π x
LHD of f(x)
where x = k - h
= (-1)k (k - 1)π
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