PG entrance exam CUET PG 2025 Mock Test Mathematical Science Analysis Continuity & Differentiability
Let f(x) = cos(x) and g(x) = \( 1-\frac{x^2}{2}\) for x ∈ \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\). Then
1
f(x) ≥ g(x) for all x ∈ \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
2
f(x) ≤ g(x) for all x ∈ \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
3
f(x) − g(x) changes sign exactly once on \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
4
f(x) − g(x) changes sign more than once on \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)