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  • Let [x] denotes the greatest integer less than or equal to x. If ,<img alt="\mathrm{ f(x)=[x \sin \pi x] }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20f%28x%29%3D%5Bx%

Let [x] denotes the greatest integer less than or equal to x. If ,\mathrm{ f(x)=[x \sin \pi x] } then f(x) is :

Option: 1

\ continuous at  x=0


Option: 2

 continuous in (-1,0)


Option: 3

 differentiable at x=1


Option: 4

 differentiable in (-1,1)


Answers (1)

best_answer


\mathrm{ From the graph, 0 \leq x \sin (\pi x)<1 }
\mathrm{ for x \in[-1,1] Hence, f(x)=0, x \in[-1,1] }

Posted by

vishal kumar

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