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Differentiation of Derivatives — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsDifferentiation of Derivatives1 Mark
Question
If the function $f(x)=\left\{\begin{array}{cl}\frac{x^2-1}{x-1}, & \text { when } x \neq 1 \\ k, & \text { when } x=1\end{array}\right.$ is given to be continuous at $x=1$, then the value of $k$ is _________________
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Answer

2 , because
$\begin{aligned} k & =\lim _{x \rightarrow 1} \frac{x^2-1}{x-1} \\ & =\lim _{x \rightarrow 1} \frac{(x+1)(x-1)}{x-1} \quad(x \neq 1) \\ & =\lim _{x \rightarrow 1} x+1 \\ & =1+1 \\ & =2 .\end{aligned}$

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