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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
$f (x)=\left\{\begin{array}{ll}\frac{x^2-4}{x-2}+ a , & \text { for } x<2 \\ 8, & \text { for } x=2 \\ x+ b +4, & \text { for } x>2\end{array}\right.$ is continuous at $x=2$, then the values of a and b are respectively
  • A
    2,4
  • ✓
    4,2
  • C
    1,2
  • D
    2,2
✓

Answer

Correct option: B.
4,2
(B)
Since $f (x)$ is continuous at $x=2$.
$\therefore \quad f (2)=\lim _{x \rightarrow 2^{-}} f (x)$
$\Rightarrow f (2)=\lim _{x \rightarrow 2}\left(\frac{x^2-4}{x-2}+ a \right) \Rightarrow 8=4+ a$
$\Rightarrow a =4$
Also, $f (2)=\lim _{x \rightarrow 2^{+}} f (x)$
$\Rightarrow f (2)=\lim (x+ b +4) \Rightarrow 8=6+ b$
$\Rightarrow b =2$

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