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प्रश्न
The function \[f\left( x \right) = \begin{cases}\frac{e^{1/x} - 1}{e^{1/x} + 1}, & x \neq 0 \\ 0 , & x = 0\end{cases}\]
पर्याय
is continuous at x = 0
is not continuous at x = 0
is not continuous at x = 0, but can be made continuous at x = 0
none of these
उत्तर
is not continuous at x = 0
Given:
We have
If \[e^\frac{1}{x} = t\] , then
\[x \to 0, t \to \infty\]
Also,
\[\therefore \lim_{x \to 0} f\left( x \right) \neq f\left( 0 \right)\]
Hence,
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