For what value of ‘k’ is the function f(x) = 5x 3x + x, & if & x … - Vidyadip

Question

For what value of ‘k’ is the function $\text{f(x)} = \begin{cases} \frac{\sin \text{5x}}{\text{3x}} + \cos \text{x}, & \text{if }& \text{x} \neq 0 \\ \text{ }\text{ }\text{ }\text{ } \text{k}, & \text{if } & \text{x = 0}\\ \end{cases}$ continuous at x = 0?

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Answer

$\lim\limits_{\text{x} \rightarrow 0} \bigg(\frac{\sin \text{5x}}{\text{3x}} + \cos \text{x} \bigg) = \frac{8}{3} \Rightarrow \text{k} = \frac{8}{3}$

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