Show that, (sin x)/(x) decreases steadil...

Show that, `(sin x)/(x)` decreases steadily and `(tan x)/(x)` increases monotonically in `0 lt x lt (pi)/(2)` and also `(tan x)/(x) gt (sin x)/(x)`.

Similar Questions

Explore conceptually related problems

For all x in 0 le x le (pi)/(2) , show that, cos(sin x) > sin(cos x)

If 0 lt x lt pi/2 , show that, sin x gt x -x^(3)/(3!)

If 0 lt x lt pi/2 , show that, cos x gt 1-x^(2)/(2!)

If x gt 0 , show that, x gt sin x

underset(x to 0)"Lt" (tan ax)/(sin bx)

If 0 lt x lt pi/2 , show that, sin x lt x lt tan x

Find f'(x)" if "f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x

Solve tan x lt 2 .

Solve (dy)/(dx) + y = tan x (0 le x lt (pi)/(2))