Evaluate
Answers
Explanation:
This page introduces various useful commands for rendering math in LaTeX, as well as instructions for building your own commands.
Contents
1 Subscripts and Superscripts
2 Math Commands
2.1 Fractions
2.2 Radicals
2.3 Sums, Products, Limits and Logarithms
2.4 Mods
2.5 Combinations
2.6 Trigonometric Functions
2.7 Calculus
2.8 Overline and Underline
3 LaTeX
3.1 Other Functions
4 Matrices
5 Text Styles in Math Mode
6 How to Build Your Own Commands
7 See Also
Subscripts and Superscripts
Subscripts and superscripts (such as exponents) can be made using the underscore _ and carat ^ symbols respectively.
Symbol Command Symbol Command
$2^{2}$ 2^2 $\textstyle a_i$ a_i
$\textstyle 2^{23}$ 2^{23} $\textstyle n_{i-1}$ n_{i-1}
$a^{i+1}_3$ a^{i+1}_3 $x^{3^2}$ x^{3^2}
$2^{a_i}$ 2^{a_i} $2^a_i$ 2^a_i
Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than one character, you must surround with curly braces. For example, x^10 produces $x^10$, while x^{10} produces $x^{10}$.
Math Commands
Here are some commonly used math commands in LaTeX:
Fractions
Symbol Command
$\frac {1}{2}$ \frac{1}{2} or \frac12
$\frac{2}{x+2}$ \frac{2}{x+2}
$\frac{1+\frac{1}{x}}{3x + 2}$ \frac{1+\frac{1}{x}}{3x + 2}
Notice that with fractions with a 1-digit numerator and a 1-digit denominator, we can simply group the numerator and the denominator together as one number. However, for fractions with either a numerator or a denominator that requires more than one character (or if the numerator starts with a letter), you need to surround everything in curly brackets.
Use \cfrac for continued fractions.
Expression Command
$\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}$ \cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}
Radicals
Symbol Command
$\sqrt{3}$ \sqrt{3}
$\sqrt{x+y}$ \sqrt{x+y}
$\sqrt{x+\frac{1}{2}}$ \sqrt{x+\frac{1}{2}}
$\sqrt[3]{3}$ \sqrt[3]{3}
$\sqrt[n]{x}$ \sqrt[n]{x}
Sums, Products, Limits and Logarithms
Use the commands \sum, \prod, \lim, and \log respectively. To denote lower and upper bounds, or the base of the logarithm, use _ and ^ in the same way they are used for subscripts and superscripts. (Lower and upper bounds for integrals work the same way, as you'll see in the calculus section)
Symbol Command
$\textstyle \sum_{i=1}^{\infty}\frac{1}{i}$ \sum_{i=1}^{\infty}\frac{1}{i}
$\textstyle \prod_{n=1}^5\frac{n}{n-1}$ \prod_{n=1}^5\frac{n}{n-1}
$\textstyle \lim_{x\to\infty}\frac{1}{x}$ \lim_{x\to\infty}\frac{1}{x}
$\textstyle \lim\limits_{x\to\infty}\frac{1}{x}$ \lim\limits_{x\to\infty}\frac{1}{x}
$\textstyle \log_n n^2$ \log_n n^2
Some of these are prettier in display mode:
Symbol Command
$\sum_{i=1}^{\infty}\frac{1}{i}$ \sum_{i=1}^{\infty}\frac{1}{i}
$\prod_{n=1}^5\frac{n}{n-1}$ \prod_{n=1}^5\frac{n}{n-1}
$\lim_{x\to\infty}\frac{1}{x}$ \lim_{x\to\infty}\frac{1}{x}
Note that we can use sums, products, and logarithms without _ or ^ modifiers.
Symbol Command
$\sum\frac{1}{i}$ \sum\frac{1}{i}
$\frac{n}{n-1}$ \frac{n}{n-1}
$\textstyle \log n^2$ \log n^2
$\textstyle \ln e$ \ln e
Mods
Symbol Command
$9\equiv 3 \bmod{6}$ 9\equiv 3 \bmod{6}
$9\equiv 3 \pmod{6}$ 9\equiv 3 \pmod{6}
$9\equiv 3 \mod{6}$ 9\equiv 3 \mod{6}
$9\equiv 3\pod{6}$ 9\equiv 3 \pod{6}
Combinations