- 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