Inequality

Prove that $\sin x + 2x \ge \frac{3x.(x+1)}{\pi}$ for x $(0, \dfrac{π}{2} )$

#Calculus

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Use the graph $y=sin(x)$ from 0 to $\pi/2$ the graph is always above y= $\frac{2*x}{\pi}$ that is the straight line passing through origin and ( $\pi/2$ ,0).Now you get sin x >= $\frac{2*x}{\pi}$ in the given interval.Now use this thing and proceed ....x will cancel out in next step and u will get that $\frac{2\pi-1}{3}$ >=x which is true in the interval that is given in the problem. Hope it helps. :)

rajdeep brahma - 2 years, 12 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$