Find the minimum of 9 x sin x + 4/ ( x sin x ) for x ∈ ( 0 , π ) .

Start Free Mock LoginAlready registered? Login here

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumsingle choice

Find the minimum of $9 x sin x + 4/ (x sin x)$ for $x \in (0, π)$ .

Options:

Answer:

Solution:

Let $t = x sin x > 0$ . AM-GM gives $9 t + 4/ t \geq 12$ , with equality at $t = 2/3$ . By continuity, $x sin x$ takes that value between 0 and $π /2$ , so the minimum 12 is attained.

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Means / inequality

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...