Solveeit Logo
Login

Question

Question: Let x Ī\(\left( 0,\frac{\pi}{2} \right)\), f(x) = x tan(sin x), g(x) = xsin(tanx) and h(x) = sinx ta...

Let x Ī(0,π2)\left( 0,\frac{\pi}{2} \right), f(x) = x tan(sin x), g(x) = xsin(tanx) and h(x) = sinx tanx. Which one is greatest ?

A

f(x)

B

g(x)

C

h(x)

D

Depends on x

Answer

h(x)

Explanation

Solution

x < tan x and sinx/x decreases Ž h(x) > g(x)

sin x < x and tanx/x increases Ž h(x) > f(x)