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प्रश्न
Discuss the continuity of the following functions at the indicated point(s):
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उत्तर
Given:
\[f\left( x \right) = \binom{\left| x - a \right|\sin\left( \frac{1}{x - a} \right), for x \neq a}{0, for x = a}\]
\[\Rightarrow f\left( x \right) = \begin{cases}\left( x - a \right)\sin\left( \frac{1}{x - a} \right), x > 0 \\ \left( x + a \right)\sin\left( \frac{1}{x + a} \right), x < 0 \\ 0, x = a\end{cases}\]
We observe
(LHL at x = a) =
(RHL at x = a) =
Hence, f(x) is continuous at x = a.
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