\left. \begin{array} { l } { 53 } \\ { 5 } \\ { 25 } \\ { 32 } \\ { 256 } \\ { 356 } \\ { 177 } \\ { 477 } \\ { 46 } \\ { 168 } \\ { 19 } \\ { 20 } \end{array} \right.
Sort
5,19,20,25,32,46,53,168,177,256,356,477
Evaluate
53,\ 5,\ 25,\ 32,\ 256,\ 356,\ 177,\ 477,\ 46,\ 168,\ 19,\ 20
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53
To sort the list, start from a single element 53.
5,53
Insert 5 to the appropriate location in the new list.
5,25,53
Insert 25 to the appropriate location in the new list.
5,25,32,53
Insert 32 to the appropriate location in the new list.
5,25,32,53,256
Insert 256 to the appropriate location in the new list.
5,25,32,53,256,356
Insert 356 to the appropriate location in the new list.
5,25,32,53,177,256,356
Insert 177 to the appropriate location in the new list.
5,25,32,53,177,256,356,477
Insert 477 to the appropriate location in the new list.
5,25,32,46,53,177,256,356,477
Insert 46 to the appropriate location in the new list.
5,25,32,46,53,168,177,256,356,477
Insert 168 to the appropriate location in the new list.
5,19,25,32,46,53,168,177,256,356,477
Insert 19 to the appropriate location in the new list.
5,19,20,25,32,46,53,168,177,256,356,477
Insert 20 to the appropriate location in the new list.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}