If f ( x ) = x sin 1 x , where x 0 , then the value of the function f at x = 0 , so that the function is continuous at x = 0 , is:

Question

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

Smart Achievers · Accepted Answer

(1)

Ans. 0

Explanation:

We have $f (x) = x \sin \frac{1}{x},$ where $x \neq 0 .$

Since, $f (x)$ is continuous at $x = 0$ ,

we must have $\lim_{x \to 0} x \sin \frac{1}{x} = f (0)$

$∴$ $f (0) = 0 \times$ [an oscillating value between - 1 and 1]

$∴$ $f (0) = 0$

Solution

Q.
If $f (x) = x \sin \frac{1}{x}$ , where $x \neq 0$ , then the value of the function $f$ at $x = 0$ , so that the function is continuous at $x = 0$ , is:

1 0

2 - 1

3 1

4 None of these

Ans.
(1)

Ans. 0

Explanation:

We have $f (x) = x \sin \frac{1}{x},$ where $x \neq 0 .$

Since, $f (x)$ is continuous at $x = 0$ ,

we must have $\lim_{x \to 0} x \sin \frac{1}{x} = f (0)$

$∴$ $f (0) = 0 \times$ [an oscillating value between - 1 and 1]

$∴$ $f (0) = 0$

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