Taylor and Maclaurin Series of Sin Function
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Series@Sin@xD, 8x, 0, 4<D x - x 3 6 + O@xD 5 Series@Sin@xD, 8x, 1, 6<D Sin@1D + Cos@1DHx - 1L - 1 2 Sin@1DHx - 1L 2 - 1 6 Cos@1DHx - 1L 3 + 1 24 Sin@1DHx - 1L 4 + 1 120 Cos@1DHx - 1L 5 - 1 720 Sin@1DHx - 1L 6 + O@x - 1D 7 Normal@%D H- 1 + xL Cos@1D - 1 6 H- 1 + xL 3 Cos@1D + 1 120 H- 1 + xL 5 Cos@1D + Sin@1D - 1 2 H- 1 + xL 2 Sin@1D + 1 24 H- 1 + xL 4 Sin@1D - 1 720 H- 1 + xL 6 Sin@1D Plot@%, 8x, 0, 10<D 2 4 6 8 10 -80 -60 -40 -20
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This Document consist of Mathematica commands for plotting taylor and maclaurin series for the sin function.
Transcript of Taylor and Maclaurin Series of Sin Function
Series@Sin@xD, 8x, 0, 4<D
x -
x3
6
+ O@xD5
Series@Sin@xD, 8x, 1, 6<D
Sin@1D + Cos@1D Hx - 1L -
1
2
Sin@1D Hx - 1L2-
1
6
Cos@1D Hx - 1L3+
1
24
Sin@1D Hx - 1L4+
1
120
Cos@1D Hx - 1L5-
1
720
Sin@1D Hx - 1L6+ O@x - 1D7
Normal@%D
H-1 + xL Cos@1D -
1
6
H-1 + xL3Cos@1D +
1
120
H-1 + xL5Cos@1D +
Sin@1D -
1
2
H-1 + xL2Sin@1D +
1
24
H-1 + xL4Sin@1D -
1
720
H-1 + xL6Sin@1D
Plot@%, 8x, 0, 10<D
2 4 6 8 10
-80
-60
-40
-20