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Question
Prove that the function
Solution
The given function can be rewritten as:
We observe
(LHL at x = 0) =
(RHL at x = 0) =
So,
\[\lim_{x \to 0^-} f\left( x \right) \text{and} \lim_{x \to 0^+} f\left( x \right)\]
Thus, f(x) is discontinuous at x = 0, regardless of the choice of k.
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