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  • If f(x) = x^2 \sin 1/x where , then the value of the function f at x = 0, so that the function is continuous at x = 0, is A. 0 B. -1 C. 1 D. None of these

If  f(x) = x^2 \sin \frac{1}{x}  where  , then the value of the function f at x = 0, so that the function is continuous at x = 0, is

A. 0

B. -1

C. 1

D. None of these

Answers (1)

A)

We have, f(x) = x^2 \sin \frac{1}{x} where x ≠ 0.

Given that, the function is continuous at x = 0

\begin{aligned} &\lim _{x \rightarrow 0} f(x)=f(0)\\ &\lim _{x \rightarrow 0} x^{2} \sin \frac{1}{x}=f(0)\\ &\Rightarrow f(0)=0 \times(\text { an oscillating number between }-1 \text { and } 1)\\ &\Rightarrow f(0)=0 \end{aligned}

Hence, the value of the function f at x = 0 is ‘0’.

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