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  • If <img alt="\mathrm{f(x)=x \sin \left(\frac{1}{x}\right), x \neq 0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3Dx%20%5Csin%20%5Cleft%28%5Cfrac%7B1%7D%7Bx%7D%5Crigh

If \mathrm{f(x)=x \sin \left(\frac{1}{x}\right), x \neq 0}, then the value of the function at. x=0, so that the function is continuous at x=0 is.

Option: 1

1


Option: 2

-1


Option: 3

0


Option: 4

Indeterminate.


Answers (1)

best_answer

Since f(x) is continuous at x=0, therefore
\mathrm{ f(0)=\lim _{x \rightarrow 0} x \sin \left(\frac{1}{x}\right)=0 }

Posted by

Divya Prakash Singh

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