$$\lim_{x\to0}\left(\frac{x-\sin\left(x\right)}{1-\sin\left(x\right)}\right)$$

$$x\frac{dy}{dx}=\frac{cos\left(8x\right)}{x}-2y$$

$$\lim_{x\to\infty}\left(\frac{1}{3}.\sqrt{5x^6-2}\right)$$

$$\left(x^3-x^2+4x+2\right)\cdot\left(x^3-2x+8\right)$$

$$5xy\left(4x-3y\right)$$

$$\frac{dy}{dx}=\frac{9-y^2}{10}$$

$$\frac{3x^2-8}{x+2}$$