$\lim_{x\to0}\left(\frac{x^2+1}{x^2-1}\right)^x$

$\lim_{x\to1000}\left(n\:\cdot\:\sin\left(\frac{\pi}{n}\right)\right)$

$x^2-3x=7$

$\log\left(2x-5\right)+\log\left(2x+5\right)=2\log\left(x\right)+\log\left(3\right)$

$y=\arctan\left(\frac{x}{7}\right)+\frac{3x-9}{7\left(x^2+2\right)}$

$\lim_{x\to\infty}x^{\frac{x}{2}}$

$\lim_{x\to0}\left(\frac{\tan\left(3x\right)^2}{2x}\right)$