Let \( f(x)=\tan ^{-1}\left(1+x+x^{2}+\ldots \ldots+\infty\right), ... VIDEO
Let \( f(x)=\tan ^{-1}\left(1+x+x^{2}+\ldots \ldots+\infty\right), g(x)=\cot ^{-1}\left(\frac{1}{1-x+x^{2}-x^{3}+\ldots .+\infty}\right) \), then
P
W find the correct statement \( \forall x \in(0,1) \) :
(a) Range of \( f(x) \in\left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)
(b) Range of \( f(x) \in\left(0, \frac{\pi}{4}\right) \)
(c) Range of \( g(x) \in\left(\cot ^{-1} 2, \frac{\pi}{4}\right) \)
(d) Range of \( g(x) \in\left(\frac{\pi}{4}, \pi\right) \)
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