If $f(x)\left\{\begin{array}{l}x^a \sin \frac{1}{x} & x \neq 0 \\ 0 & x=0\end{array}\right.$ is continuous. At x = 0, then
Answer & explanation
Correct answer: option 1
f(x) is continuous at x = 0 hence
$\lim\limits_{x \rightarrow 0} x^a \sin \frac{1}{x}=f(0)=0$
If a>0, then x^a will teends towards 0.
This is only possible when a > 0, thus the required set of values of a is (0, ∞)
Hence (1) is the correct answer.