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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If function $f(x)=\left\{\begin{array}{r}\frac{x^2-1}{x-1}, \text { when } x \neq 1 \\ k, \text { when } x=1\end{array}\right.$ is continuous at $x=1$, then the value of k will be
  • A
    -1
  • ✓
    2
  • C
    -3
  • D
    -2
✓

Answer

Correct option: B.
2
(B)
Since $f (x)$ is continuous at $x=1$.
$\therefore \quad f (1)=\lim _{x \rightarrow 1} f (x)$
$\Rightarrow k =\lim _{x \rightarrow 1} \frac{x^2-1}{x-1}$
$\Rightarrow k =\lim _{x \rightarrow 1}(x+1)$
$\Rightarrow k =2$

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