$\lim_{x\to\infty}\left(\frac{x^2-2x-3}{x+1}\right)$

$-7-1+2$

$\lim_{x\to3}\left(\left(x-3\right)^{x-3}\right)$

$\frac{-2}{x}-4<1$

$4x\left(x-3\right)$

$2sin^{\left(2\right)}\theta\:+cos\left(\frac{\pi}{2}-\theta\:\right)=1$

$1+\frac{tan\left(x\right)}{\cot\left(x\right)}=\sec\left(x\right)$