\left. \begin{array} { l } { 53 } \\ { 52 } \\ { 53 } \\ { 54 } \\ { 50 } \\ { 52 } \\ { 49 } \\ { 48 } \\ { 51 . } \\ { 53 } \\ { 51 } \\ { 54 } \\ { 53 } \\ { 9 } \end{array} \right.
Sort
9,48,49,50,51,51,52,52,53,53,53,53,54,54
Evaluate
53,\ 52,\ 53,\ 54,\ 50,\ 52,\ 49,\ 48,\ 51,\ 53,\ 51,\ 54,\ 53,\ 9
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53
To sort the list, start from a single element 53.
52,53
Insert 52 to the appropriate location in the new list.
52,53,53
Insert 53 to the appropriate location in the new list.
52,53,53,54
Insert 54 to the appropriate location in the new list.
50,52,53,53,54
Insert 50 to the appropriate location in the new list.
50,52,52,53,53,54
Insert 52 to the appropriate location in the new list.
49,50,52,52,53,53,54
Insert 49 to the appropriate location in the new list.
48,49,50,52,52,53,53,54
Insert 48 to the appropriate location in the new list.
48,49,50,51,52,52,53,53,54
Insert 51 to the appropriate location in the new list.
48,49,50,51,52,52,53,53,53,54
Insert 53 to the appropriate location in the new list.
48,49,50,51,51,52,52,53,53,53,54
Insert 51 to the appropriate location in the new list.
48,49,50,51,51,52,52,53,53,53,54,54
Insert 54 to the appropriate location in the new list.
48,49,50,51,51,52,52,53,53,53,53,54,54
Insert 53 to the appropriate location in the new list.
9,48,49,50,51,51,52,52,53,53,53,53,54,54
Insert 9 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}