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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f(x)=\left\{\begin{array}{c}x^2 \sin \frac{1}{x} ; \text { when } x \neq 0 \\ 0 ; \text { when } x=0\end{array}\right.$, then
  • A
    $\lim _{x \rightarrow 0^{+}} f(x)=1$
  • B
    $\lim _{x \rightarrow 0^{-}} f(x)=-1$
  • ✓
    $f (x)$ is continuous at $x=0$
  • D
    $f (x)$ is discontinuous at $x=0$
✓

Answer

Correct option: C.
$f (x)$ is continuous at $x=0$
(C)
$\lim _{x \rightarrow 0} f(x)-\lim _{x \rightarrow 0} x^2 \sin \frac{1}{x}$, but $-1 \leq \sin \frac{1}{x} \leq 1$ and $x \rightarrow 0$
$\therefore \quad \lim _{x \rightarrow 0^{+}} f (x)=0=\lim _{x \rightarrow 0^{-}} f (x)= f (0)$
$\therefore f (x)$ is continuous at $x=0$.

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