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Question

If fx=x2sin1x, where x ≠ 0, 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

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Solution


The given function is fx=x2sin1x, where x ≠ 0.

Now, f(x) is continuous at x = 0.

f0=limx0fx

f0=limx0x2sin1x

f0=limx0x2×limx0sin1x

⇒ f(0) = 0 × a finite value between − 1 and 1 -1sin1x1

⇒ f(0) = 0

Thus, the value of the function f at x = 0 so that the function is continuous at x = 0 is 0.

Hence, the correct answer is option (a).

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