Definition of Convex Set A set is convex if the line segment joining any two points in the set lies entirely within the set. 2. Convex Shapes Ellipses, circles, and half-planes are convex. 3. Non-Convex Shape Parabolas do not define convex regions when used in inequalities of the form $y \le f(x)$ or $y \ge f(x)$ where $f(x)$ is a strictly convex or concave function. 4. Testing Convexity Choose two points in the set and check if their midpoint (or any point on the segment connecting them) lies within the set. If even one such segment has a point outside the set, the set is not convex. 407. The Fourier transform of the function f(x) = - Question not attempted

Asked in Asst. Statistical Officer (Agri. Deptt.) 2024 · Topic: Mechanics (Newton's Laws of Motion and their applications)

1. $\frac{1}{2\sqrt{2}\text{as} ^2}\sin^2\left(\frac{\text{as}}{2}\right)$
2. $\frac{2\sqrt{2}\cos^2\left(\frac{\text{as}} {2}\right)}{\sqrt{\pi}\text{as}^2}$
3. $\frac{2\sqrt{2}\sin^2\left(\frac{\text{as}} {2}\right)}{\sqrt{\pi}\text{as}^2}$
4. $\frac{2\sqrt{2}}{\sqrt{\pi}\text{as} ^2}\sin\left(\frac{\text{as}}{2}\right)$

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