$\lim_{x\to\infty}\left(\sqrt{x+1}-\sqrt[3]{x}\right)$

$5\cdot\sqrt[2]{1}$

$\lim_{x\to\infty}\left(\frac{arctan\left(x^2\right)}{x^5}\right)$

$\int\frac{12\left(x+5\right)}{\left(x-5\right)\left(x^2-1\right)}dx$

$\frac{x^2+2}{x^3+9x^2+27x+27}$

$\lim_{h\to0}\:\left(\frac{\left(c+h\right)^2-c^2}{h}\right)$

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