Question

In `(0, pi/2),`  the function f (x) = `"x"/"sin x"` is ____________.

Options

• a decreasing function

• a constant function

• an increasing function

• none of these

Answer 1

In `(0, pi/2),`  the function f (x) = `"x"/"sin x"` is an increasing function.

Explanation:

`"f'" ("x") = ("sinx - x cos x")/("sin"^2 "x") = "cos x"/("sin"^2 "x") ("tan x - x") > 0`

Hence an increasing function.