Determine the value of the constant ‘k’ so that the function f(x)… - Vidyadip

Question

Determine the value of the constant ‘k’ so that the function $\text{f}(x) = \begin{cases} \frac{\text{k}x}{| x|}\text{ }\text{ }, & \text{if } x < 0\\ \text{ }3\text{ }\text{ }\text{ }\text{ }, & \text{if } x\geq 0\\ \end{cases}$ is continuous at x = 0.

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Answer

$\lim\limits_{\text{x} \rightarrow 0_{-}} \text{f(x)} = \lim\limits_{\text{x} \rightarrow 0_{-}} \frac{\text{kx}}{|\text{x}|} = \text{-k}$
$\text{k = -3}$

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