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If a function $f(x)$ defined on $[a, b]$ is discontinuous at $x=\alpha \in(a, b)$, then
Options:
Solution:
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Verified Answer
The correct answer is:
$\lim _{x \rightarrow \alpha^{+}} f(x) \neq f(\alpha)$
$f(x)$ is defined on $[a, b]$ and discontinuous at $x=\alpha \in(a, b)$
Since $f(x)$ is discontinuous at $x=\alpha \in(a, b)$
Hence option (a) will never be true
but $\lim _{x \rightarrow \alpha} f(x) \neq f(\alpha)$ is showing that $f(x)$ is discontinuous
at $x=\alpha \in(a, b)$
Hence option (b) is correct.
Since function is not defined for $x \rightarrow a^{-}$. Hence option (c) is incorrect.
Since function is not defined when $x \rightarrow b^{+}$. Hence (d) is incorrect.
Since $f(x)$ is discontinuous at $x=\alpha \in(a, b)$
Hence option (a) will never be true
but $\lim _{x \rightarrow \alpha} f(x) \neq f(\alpha)$ is showing that $f(x)$ is discontinuous
at $x=\alpha \in(a, b)$
Hence option (b) is correct.
Since function is not defined for $x \rightarrow a^{-}$. Hence option (c) is incorrect.
Since function is not defined when $x \rightarrow b^{+}$. Hence (d) is incorrect.
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