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Question

The left-hand derivative of f(x)=[x]sin(πx) at x=k, k an integer and [x]= greatest integer x, 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]sinπ(kh)[k]sinπkh
=limh0(1)k1(k1)sinπhk×0h
=limh0(1)k1.(k1)sinπhh
=(1)k.(k1)π.

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