\lim _(x\to \infty )\left((tanx-sinx)/(x^2)\right)

Question

`\lim _(x\to \infty )\left((tanx-sinx)/(x^2)\right)`

Answer 1

The limit does not exist. There are infinitely many infinite discontinuities at
`x=n\pi`, where
`n\in\Bbb N`. The function oscillates wildly between negative and positive infinity.