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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If the function $f(x)=\left\{\begin{array}{cc}5 x-4, & \text { if } 0< x \leq 1 \\ 4 x^2+3 b x, & \text { if } 1< x< 2\end{array}\right.$ is continuous at every point of its domain, they value of $b$ is
  • ✓
    -1
  • B
    $0$
  • C
    1
  • D
    none of these
✓

Answer

Correct option: A.
-1
(A)
Since $f (x)$ is continuous at every point of its domain.
∴ it is continuous at $x=1$.
$\therefore \quad \lim _{x \rightarrow 1^{-}} f (x)=\lim _{x \rightarrow 1^{+}} f (x)$
$\Rightarrow \lim _{x \rightarrow 1}(5 x-4)=\lim _{x \rightarrow 1}\left(4 x^2+3 b x\right)$
$\Rightarrow 1=4+3 b \Rightarrow b=-1$

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