\left. \begin{array} { c } { 42 } \\ { 42 } \\ { 25 } \\ { 42 } \\ { 23 } \\ { 48 } \\ { 71 } \\ { 389 } \\ { 54 } \\ { 55 } \\ { 249 } \\ { 499 } \end{array} \right.
Sort
23,25,42,42,42,48,54,55,71,249,389,499
Evaluate
42,\ 42,\ 25,\ 42,\ 23,\ 48,\ 71,\ 389,\ 54,\ 55,\ 249,\ 499
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42
To sort the list, start from a single element 42.
42,42
Insert 42 to the appropriate location in the new list.
25,42,42
Insert 25 to the appropriate location in the new list.
25,42,42,42
Insert 42 to the appropriate location in the new list.
23,25,42,42,42
Insert 23 to the appropriate location in the new list.
23,25,42,42,42,48
Insert 48 to the appropriate location in the new list.
23,25,42,42,42,48,71
Insert 71 to the appropriate location in the new list.
23,25,42,42,42,48,71,389
Insert 389 to the appropriate location in the new list.
23,25,42,42,42,48,54,71,389
Insert 54 to the appropriate location in the new list.
23,25,42,42,42,48,54,55,71,389
Insert 55 to the appropriate location in the new list.
23,25,42,42,42,48,54,55,71,249,389
Insert 249 to the appropriate location in the new list.
23,25,42,42,42,48,54,55,71,249,389,499
Insert 499 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}