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Question

The left-hand derivative of f(x)=[x]sin(πx) at x= k, k is an integer and [x] = greatest integer, is

A
(1)k(k1)π
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B
(1)k1(k1)π
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C
(1)kkπ
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D
(1)k1kπ
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Solution

The correct option is A (1)k(k1)π
f(k0)=limh0[kh]sin π(kh)[k]sin πkh
=limh0(1)k1(k1)sinπhk×0h
=limh0(1)k1(k1)sin πhh=(1)k.(k1)π

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