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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
For the function $f(x)=\left\{\begin{array}{r}\frac{\sin ^2 a x}{x^2}, \text { when } x \neq 0 \\ 1, \text { when } x=0\end{array}\right.$ which one is a true statement?
  • A
    $f (x)$ is continuous at $x=0$, when $a \neq \pm 1$
  • ✓
    $f (x)$ is discontinuous at $x=0$, when $a \neq \pm 1$
  • C
    $\lim _{x \rightarrow 0} f (x)= a$
  • D
    $\lim _{x \rightarrow 0} f(x)=a^3$
✓

Answer

Correct option: B.
$f (x)$ is discontinuous at $x=0$, when $a \neq \pm 1$
(B)
$\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} \frac{\sin ^2 a x}{(a x)^2} a^2=a^2$ and $f(0)=1$.
$\therefore f (x)$ is discontinuous at $x=0$, when $a \neq \pm 1$

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