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Differentiation of Derivatives — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsDifferentiation of Derivatives2 Marks
Question
If the following function $f(x)$ is continuous at $x=0$, then write the value of $k$.
$f(x)=\left\{\begin{array}{cc}\frac{\sin \frac{3 x}{2}}{x}, & x \neq 0 \\ k, & x=0\end{array}\right.$
✓

Answer

$\lim _{x \rightarrow 0} \frac{\sin \frac{3 x}{2}}{x}=\lim _{x \rightarrow 0} \frac{3}{2} \cdot \frac{\sin \frac{3 x}{2}}{\frac{3 x}{2}}=\frac{3}{2}$
or $k=\frac{3}{2} . \quad\left[\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\right]$

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