\left. \begin{array} { r } { 72 } \\ { 35 } \\ { 75 } \\ { 20 } \\ { 325 } \\ { 720 } \\ { 30 } \\ { 100 } \\ { 60 } \\ { 55 } \\ { 55 } \\ { 20 } \\ { 120 } \\ { 20 } \end{array} \right.
Sort
20,20,20,30,35,55,55,60,72,75,100,120,325,720
Evaluate
72,\ 35,\ 75,\ 20,\ 325,\ 720,\ 30,\ 100,\ 60,\ 55,\ 55,\ 20,\ 120,\ 20
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72
To sort the list, start from a single element 72.
35,72
Insert 35 to the appropriate location in the new list.
35,72,75
Insert 75 to the appropriate location in the new list.
20,35,72,75
Insert 20 to the appropriate location in the new list.
20,35,72,75,325
Insert 325 to the appropriate location in the new list.
20,35,72,75,325,720
Insert 720 to the appropriate location in the new list.
20,30,35,72,75,325,720
Insert 30 to the appropriate location in the new list.
20,30,35,72,75,100,325,720
Insert 100 to the appropriate location in the new list.
20,30,35,60,72,75,100,325,720
Insert 60 to the appropriate location in the new list.
20,30,35,55,60,72,75,100,325,720
Insert 55 to the appropriate location in the new list.
20,30,35,55,55,60,72,75,100,325,720
Insert 55 to the appropriate location in the new list.
20,20,30,35,55,55,60,72,75,100,325,720
Insert 20 to the appropriate location in the new list.
20,20,30,35,55,55,60,72,75,100,120,325,720
Insert 120 to the appropriate location in the new list.
20,20,20,30,35,55,55,60,72,75,100,120,325,720
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}