CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=x+\cot ^{-1} x\) is increasing in the interval:
- A \((-\infty, \infty)\)
- B \((-1, \infty)\)
- C \((0, \infty)\)
- D \((1, \infty)\)
Answer & Solution
Correct Answer
(A) \((-\infty, \infty)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 1 - \frac{1}{1+x^2}\) \(f'(x) = \frac{1+x^2-1}{1+x^2} = \frac{x^2}{1+x^2}\) For increasing function, \(f'(x) \ge 0\). \(\frac{x^2}{1+x^2} \ge 0\) Since \(x^2 \ge 0\) and \(1+x^2 > 0\) for all real \(x\), \(f'(x) \ge 0\) for all \(x \in \mathbb{R}\). Interval:…
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