If \( f(\theta)=\lim _{n \rightarrow \infty} \sum_{r=0}^{n \theta} \frac{2 r}{n \sqrt{(3 \theta ...
If \( f(\theta)=\lim _{n \rightarrow \infty} \sum_{r=0}^{n \theta} \frac{2 r}{n \sqrt{(3 \theta n-2 r)(n \theta+2 r)}} \) then :
(a) \( f(1)=\frac{\pi}{6} \)
(b) \( f(\theta)=\frac{\theta}{2} \int_{0}^{\theta} \frac{d x}{\sqrt{\theta^{2}-\left(x-\frac{\theta}{2}\right)^{2}}} \)
(c) \( f(\theta) \) is a constant function
(d) \( y=f(\theta) \) is invertible
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