If \( \alpha \) is the root of the equation \( x-\tan x=3 \) where \( \alpha \in\left(\frac{\pi}...

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If \( \alpha \) is the root of the equation \( x-\tan x=3 \) where \( \alpha \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right) \); then which of the following is/are correct?, (where [.] denotes the greatest integer function and \( \{ \). fractional part function).
(a) \( \lim _{x \rightarrow \alpha^{+}}\left[\frac{\max (\tan x,\{x\})}{x-3}\right]=1 \)
(b) \( \lim _{x \rightarrow \alpha^{+}}\left[\frac{\min (\tan x,\{x\})}{x-3}\right]=1 \)
(c) \( \lim _{x \rightarrow \alpha^{-}}\left[\frac{\min (\tan x,\{x\})}{x-3}\right]=0 \)
(d) \( \lim _{x \rightarrow a^{-}}\left[\frac{\max (\tan x,\{x\})}{\tan x}\right]=1 \)
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