$$ \begin{flalign} &(a) \quad \lim_{x\to0} \frac{\sin(x)}{x} && \\ &(b) \quad \int_0^{\infty} e^{-x}\ln(x) dx \\ &(c) \quad \frac{d}{dx}(\ln(x))^x \\ &(d) \quad \sum_{n=1}^{\infty} \frac{1}{n^2} \\ &(e) \quad \iint_{\textbf{R}^2} \frac{1}{1+x^2+y^2} dxdy \\ &(f) \quad \frac{dy}{dx} = xy^2 - \cos(x) \\ &(g) \quad \frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\partial y^2} = 0 \\ &(h) \quad \lim_{n\to\infty} \sqrt[n]{n!} \\ &(i) \quad \int \frac{1}{\sqrt{x^2+1}} dx \\ &(j) \quad e^{ix} = \cos(x) + i\sin(x) && \end{flalign} $$