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Fractions:
Instead of writing fractions as A / B we will use below syntax
Syntax :
\frac{numerator}{denominator}
Example –\frac{a+1}{b+1}
OUTPUT: -
Nth power:
Instead of writing powers as x ^ n which is not clear as if it is xor or power so we will use below syntax
Syntax:
x^y
Example –x^2
OUTPUT: -
Nth root:
Instead of writing roots as x^(1/N) which is not clear as if it is xor or root so we will use below syntax
Syntax:
\sqrt[N]{27}
Example –\sqrt[3]{27}
OUTPUT: -
Matrices
Instead of writing matrices as [[1, x, x^2], [1, y, y^2][1, z, z^2]] which is not very clear use below syntax
Syntax:
\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}
Example –\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}
OUTPUT: -
Definitions by cases (piecewise function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function’s domain, a sub-domain.
Syntax:
f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ n+1, & \text{if $n$ is odd} \end{cases}
Example –f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ n+1, & \text{if $n$ is odd} \end{cases}
OUTPUT: -
System of equations is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function’s domain, a sub-domain.
Syntax:
\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.
Example –\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.
OUTPUT: -
Summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total.
Syntax:
\sum_{i=0}^n i^2
Example –\sum_{i=0}^n i^2
OUTPUT: -
subscriptsis a character that is set slightly below the normal line of type.
Syntax:
\log_2 x
Example –\log_2 x
OUTPUT: -
floor is the function that takes as input a real number and gives as output the greatest integer less than or equal to, denoted.
Syntax:
\lfloor n \rfloor
Example –\lfloor 2.2 \rfloor
OUTPUT: -
ceil function maps to the least integer greater than or equal to, denoted.
Syntax:
\lceil n \rcei
Example –\lceil 2.5 \rceil
OUTPUT: -
Some Combined examples :
-
Example –
- Use
\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}
for
Example –
- Use
\left(\frac{\sqrt x}{y^3}\right)
for
Example –
- Use
\Biggl(\biggl(\Bigl(\bigl((n)\bigr)\Bigr)\biggr)\Biggr)
for
Example –
- Use
\sqrt[3]{\frac xy}
for
- Use
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