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Example 1
Add 4x4 + 3x3 - x2 + x + 6 and -7x4 - 3x3 + 8x2 + 8x - 4
We write them one below the other as shown below.
4x4 + 3x3 - x2 + x + 6
(+)
-7x4 - 3x3 + 8x2 + 8x - 4
-3x4 + 0 + 7x2 + 9x + 2
Example 2
Add 5x5 - 6x3 + 4x2 + 3x - 7, 3x5 - 2x4 + 3x2 + 6x - 1
and- 3x4 + x3 - 5x2 + 7x + 4
5x5 + - 6x3 + 4x2 + 3x - 7
3x5 - 2x4+ + 3x2 + 6x - 1
- 3x4+ x3 - 5x2 + 7x + 4
8x5 - 5x4 - 5x3 + 2x2 + 16x - 4
Example 3
Subtract -7x4 - 3x3+ 8x2 + 8x - 4 from 4x4 + 3x3 - x2 + x + 6
4x4 + 3x3- x2 + x + 6
(-)
11x4 + 6x3 - 9x2 - 7x + 10
In this problem, in some expressions we do not find terms of certain powers. They have been left as blanks.
Example 4
Subtract the first from the second and sum the difference with the third expression. The expressions are given below.
5x5 - 6x3 + 4x2 + 3x - 7, 3x5 - 2x4 + 3x2 + 6x - 1 and -3x4 + x3 - 5x2 + 7x + 4.
The difference of first two expressions is given by
3x5 - 2x4 + 3x2 + 6x - 1
5x5 - 6x3 + 4x2 + 3x - 7
-2x5 - 2x4 + 6x3 - x2 + 3x + 6
The sum of the difference between the first two expressions and the third expression will be as shown below.
(+) - 3x4+ x3 - 5x2 + 7x + 4
-2x5 - 5x4+ 7x3 - 6x2 + 10x + 10
commutative law
Question: Find Fourier series for the periodic function of period 2 π,defined by f(x) = x 4 , - π ≤ x ≤ π
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