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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f (x)=\left\{\begin{array}{c} ax ^2- b , \text { when } 0 \leq x<1 \\ 2, \text { when } x=1 \\ x+1, \text { when } l < x \leq 2\end{array}\right.$ is continuous at
$x=1$, then the most suitable values of $a , b$ are
  • A
    $a=2, b=0$
  • B
    $a=1, b=-1$
  • C
    $a=4, b=2$
  • ✓
    All the above
✓

Answer

Correct option: D.
All the above
(D)
Since $f (x)$ is continuous at $x=1$.
$\therefore \quad f (1)=\lim _{x \rightarrow 1^{-}} f (x)$
$\Rightarrow 2=\lim _{x \rightarrow 1}\left(a x^2-b\right)$
$\Rightarrow 2=a-b$
The values of $a$ and $b$ in options (A), (B) and (C) satisfies this relation.
$\therefore $ option (D) is the correct answer.

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