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  • If <img alt="f(x)\left\{\begin{array}{ll}x^a \sin \frac{1}{x} & x \neq 0 \\ 0 & x=0\end{array}\right." src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%5Cleft%5C%7B%5Cbegin%7Ba

If f(x)\left\{\begin{array}{ll}x^a \sin \frac{1}{x} & x \neq 0 \\ 0 & x=0\end{array}\right. is continuous.  At x=0, then

Option: 1

\quad a \in(0, \infty)


Option: 2

a \in(1, \infty)


Option: 3

\quad a \in(-1, \infty)


Option: 4

\quad a \in(-\infty, 1)


Answers (1)

best_answer

f(x) is continuous at x=0 hence

\lim _{x \rightarrow 0} x^{a} \sin \frac{1}{x}=f(0)=0

This is only possible when a>0, thus the required set of values of a is (0, \infty).

Hence (A) is the correct answer.

Posted by

Ajit Kumar Dubey

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