Question

find the fourierbseries representation f(x)=x+1 for -1 11 years ago

Answer 1

Do you know the Fourier series equations? What is a Fourier series?

Answer 2

\[a_k = \frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\cos(kx) dx\]\[b_k = \frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\sin(kx) dx\]\[f(x) = \frac{a_0}{2}+ \sum _{n=1}^{\infty}a_k \cos(kx)+b_ksin(kx)\]

Answer 3

\[a_0 =\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\cos(0x) dx=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x) dx\]

Answer 4

the above formulas work for a function f(x) with period 2pi. Thus it is required for the function to be defined in the interval (-pi, pi). In your question, nothing has been said about the period. Also, the given function is defined only for " 1<equal x<equal 1". so you'' have to modify the limits of integration and take only those values which are allowed by the domain.

Answer 5

ok but can you please complete it for me.... i tried solving but i got many errors please help

Answer 6

@akitav , your equations are incorrect. @GIL.ojei please refer to http://www.sosmath.com/fourier/fourier1/fourier1.html , and http://www.sosmath.com/fourier/fourier2/fourier2.html for the equations with limits [-L,L] and examples using those limits.

Answer 7

ibut it is the right question f(x)=(x+1) -1\[\le x \le1\]

Answer 8

You need to calculate your a0, an, and bn constants first. Show me what you have so far.

Answer 9

i got 1/pi -2sinpix/pi +1/sinpix/pi ..... please solve and show me what you got if possible, please find \[\int\limits_{-1}^{1}(x+1)sinx \] for bn because an is =0.. show work

Answer 10

That's not right, let's solve a0 first because it's easy. Show me your steps. The equation is \[a _{0}=\frac{ 1 }{ 2L }\int\limits_{-L}^{L} f(x)dx\]

Answer 11

ok. please solve and let me watch and learn.. please it is an exam question and do not want to do any mistake ,,, please

Answer 12

stating it is an exam question we can't help you, also it was explained very well