Consider the statements: (1) $\frac{x}{1+x^2} 0$, (2) If $0 ≤ x < \pi/2$, then $\sin x + \tan x - 3x ≥ 0$. Which are correct?
- A. Only (1)
- B. Only (2)
- C. (1) and (2)
- D. None of these
✅ Correct Answer: (1) and (2)
Explanation
Both inequalities can be verified using derivatives and standard inequality properties of $\tan^{-1}x$ and $\sin x$.
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