\left. \begin{array} { r } { 45 } \\ { 45 } \\ { 60 } \\ { 84 } \\ { 105 } \\ { 280 } \\ { 30 } \\ { 40 } \\ { 322 } \\ { 60 } \\ { 25 } \\ { 25 } \\ { 32 } \\ { 12.8 } \\ { 30 } \end{array} \right.
Sort
12.8,25,25,30,30,32,40,45,45,60,60,84,105,280,322
Evaluate
45,\ 45,\ 60,\ 84,\ 105,\ 280,\ 30,\ 40,\ 322,\ 60,\ 25,\ 25,\ 32,\ 12.8,\ 30
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45
To sort the list, start from a single element 45.
45,45
Insert 45 to the appropriate location in the new list.
45,45,60
Insert 60 to the appropriate location in the new list.
45,45,60,84
Insert 84 to the appropriate location in the new list.
45,45,60,84,105
Insert 105 to the appropriate location in the new list.
45,45,60,84,105,280
Insert 280 to the appropriate location in the new list.
30,45,45,60,84,105,280
Insert 30 to the appropriate location in the new list.
30,40,45,45,60,84,105,280
Insert 40 to the appropriate location in the new list.
30,40,45,45,60,84,105,280,322
Insert 322 to the appropriate location in the new list.
30,40,45,45,60,60,84,105,280,322
Insert 60 to the appropriate location in the new list.
25,30,40,45,45,60,60,84,105,280,322
Insert 25 to the appropriate location in the new list.
25,25,30,40,45,45,60,60,84,105,280,322
Insert 25 to the appropriate location in the new list.
25,25,30,32,40,45,45,60,60,84,105,280,322
Insert 32 to the appropriate location in the new list.
12.8,25,25,30,32,40,45,45,60,60,84,105,280,322
Insert 12.8 to the appropriate location in the new list.
12.8,25,25,30,30,32,40,45,45,60,60,84,105,280,322
Insert 30 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}