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The function $f(x)=(x-3)^2+\frac{1}{2}$ has domain $\mathrm{D}_f:(-\infty,\infty)$ and range $\mathrm{R}_f:\left[\frac{1}{2},\infty\right)$.\\

$\lim \limits_{x \to a^-} f(x)$\\

$\displaystyle{\lim \limits_{x \to a} \frac{f(x)-f(a)}{x-a}=f'(a)}$\\

$\displaystyle{\int \sin x \,dx=-\cos x + C}$\\

$\int_a^b$\\

$\int \limits_a^b$\\

$\displaystyle{\int_a^b}$\\

$\displaystyle{\int \limits_{a}^{b}x^2 \,dx=\left[\frac{x^3}{3}\right]_{a}^{b}=\frac{b^3}{3}-\frac{a^3}{3}}$\\

$\displaystyle{\sum \limits_{n=1}^{\infty}ar^n=a+ar+ar^2+ \cdots +ar^n}$\\

$\displaystyle{\int_a^b f(x) \,dx=\lim \limits_{x \to \infty} \sum \limits_{k=1}^{n} f(x_k) \cdot \Delta x}$\\

$\vec{v}=v_1 \vec{i}+v_2 \vec{j}=\langle v_1, v_2 \rangle$

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