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Question
The function f(x) = cot−1 x + x increases in the interval
Options
(1, ∞)
(−1, ∞)
(−∞, ∞)
(0, ∞)
Solution
(−∞, ∞)
\[f\left( x \right) = \cot^{- 1} x + x\]
\[f'\left( x \right) = \frac{- 1}{1 + x^2} + 1\]
\[ = \frac{- 1 + 1 + x^2}{1 + x^2}\]
\[ = \frac{x^2}{1 + x^2} \geq 0, \forall x \in R\]
\[\text { So,f(x)is increasing on } \left( - \infty , \infty \right) .\]
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