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Q.
The range of the function $f (\theta)=\frac{\sin \theta}{\theta}+\frac{\theta}{\tan \theta}, \theta \in\left(0, \frac{\pi}{2}\right)$ is equal to
Application of Derivatives
Solution:
We know that
$\frac{\sin \theta}{\theta}$ and $\frac{\theta}{\tan \theta}$ both are decreasing functions of $\theta$ in $\left(0, \frac{\pi}{2}\right)$. So maximum value, when $\theta \rightarrow 0$ is
$1+1=2$ and minimum value, when $\theta \rightarrow \frac{\pi}{2}$ is $\frac{2}{\pi}$.