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Question
Determine the value of the constant 'k' so that function f
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Solution
\[\text{ Given } , f(x) = \begin{cases}\frac{kx}{\left| x \right|} & , \text{ if } x < 0 \\ 3 & , \text{ if } x \geqslant 0\end{cases}\]
Since the function is continuous at x = 0, therefore,
\[\lim_{x \to 0^-} f(x) = \lim_{x \to 0^+} f(x) = f(0)\]
\[ \Rightarrow \lim_{x \to 0} \frac{- kx}{x} = \lim_{x \to 0} 3 = 3\]
\[ \Rightarrow - k = 3\]
\[ \Rightarrow k = - 3\]
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