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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
For the function $f(x) = \left\{ \begin{array}{l}\frac{{{{\sin }^2}ax}}{{{x^2}}},\,{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = 0\end{array} \right.$ which one is a true statement
  • A
    $f(x)$ is continuous at $x = 0$
  • ✓
    $f(x)$ is discontinuous at $x = 0$, when $a \ne \pm 1$
  • C
    $f(x)$ is continuous at $x = a$
  • D
    None of these
✓

Answer

Correct option: B.
$f(x)$ is discontinuous at $x = 0$, when $a \ne \pm 1$
b
(b) $\mathop {\lim }\limits_{x \to 0} f(x) = \frac{{{{\sin }^2}ax}}{{{{(ax)}^2}}}{a^2} = {a^2}$ and $f(0) = 1.$

Hence $f(x)$ is discontinuous at $x = 0$, when $a \ne 0$.

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