$sin\left(\frac{\pi}{3}+x\right)-sin\left(\frac{\pi}{3}-x\right)=sin\left(x\right)$

$-8x^3\:4x^2-6x$

$\lim_{x\to-\sqrt{5}}\left(\frac{x^2-2\sqrt{5}-15}{x+5}\right)$

$30.780+34.089$

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

$y\ln\left(\frac{dx}{dy}\right)=\left(\frac{y+1}{x}\right)^2$

$\lim_{x\to3}\left(\frac{\left(e^{x^3}-e^{27}\right)}{x-3}\right)$