The left-hand derivative of \[f(x)=[x]\sin (\pi x)\] at \[x=k,\,\,k\]is an integer and \[[x]\]= greatest integer \[\le x,\,\] is [IIT Screening 2001]

\[{{(-1)}^{k}}\,\,(k-1)\,\pi \]

The left-hand derivative of \[f(x)=[x]\sin (\pi x)\] at \[x=k,\,\,k\

1.	The left-hand derivative of \[f(x)=[x]\sin (\pi x)\] at \[x=k,\,\,k\]is an integer and \[[x]\]= greatest integer \[\le x,\,\] is [IIT Screening 2001]
A.	\[{{(-1)}^{k}}\,\,(k-1)\,\pi \]
B.	\[{{(-1)}^{k-1}}(k-1)\,\pi \]
C.	\[{{(-1)}^{k}}k\pi \]
D.	\[{{(-1)}^{k-1}}k\,\pi \]
Answer» B. \[{{(-1)}^{k-1}}(k-1)\,\pi \]

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The left-hand derivative of \[f(x)=[x]\sin (\pi x)\] at \[x=k,\,\,k\]is an integer and \[[x]\]= greatest integer \[\le x,\,\] is [IIT Screening 2001]

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