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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
For the function $f (x)=\left\{\begin{array}{cc}\frac{x^3- a ^3}{x- a }, & x \neq a \\ b , & x= a \end{array}\right.$
If $f (x)$ is continuous at $x= a$, then b is equal to
  • A
    $a^2$
  • B
    $2 a ^2$
  • ✓
    $3 a ^2$
  • D
    $4 a^2$
✓

Answer

Correct option: C.
$3 a ^2$
(C)
Since $f (x)$ is continuous at $x= a$.
$\therefore \quad f ( a )=\lim _{x \rightarrow a } f (x)$
$\Rightarrow b =\lim _{x \rightarrow a } \frac{x^3- a ^3}{x_{-} a }$
$\Rightarrow b =3 a ^{3-1}=3 a ^2$

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