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Continuity — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsContinuity2 Marks
Question
If $\text{f(x)}=\begin{cases}\frac{\text{x}^2-16}{\text{x}-4},&\text{if }\text{ x}\neq4\\\text{k},&\text{if }\text{ x}=4\end{cases}$ is continuous at x = 4, find k.
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Answer

Given, $\text{f(x)}=\begin{cases}\frac{\text{x}^2-16}{\text{x}-4},&\text{if }\text{ x}\neq4\\\text{k},&\text{if }\text{ x}=4\end{cases}$
If f(x) is continuous at x = 4, then
$\lim\limits_{{\text{x}}\rightarrow4}\text{f(x})=\text{f(4)}$
$\Rightarrow\lim\limits_{{\text{x}}\rightarrow4}\Big(\frac{\text{x}^2-16}{\text{x}-4}\Big)=\text{k}$
$\Rightarrow\lim\limits_{{\text{x}}\rightarrow4}\frac{(\text{x}+4)(\text{x}-4)}{(\text{x}-4)}=\text{k}$
$\Rightarrow\lim\limits_{{\text{x}}\rightarrow4}(\text{x}+4)=\text{k}$
$\Rightarrow\text{k}=8$

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