Question

="TexFormula1" title="\lim _{x\to \infty }\left(\frac{tanx-sinx}{x^2}\right)" alt="\lim _{x\to \infty }\left(\frac{tanx-sinx}{x^2}\right)" align="absmiddle" class="latex-formula">

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.