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Magazine Problem 5
In each exercise, obtain the Fourier sine series over the interval stipulated for the function given. Sketch the function that is the sum of the series obtained. Interval, \(0 < x < 2 c ;\) function, \(f(x)=c-x\)
Problem 5
In each exercise, obtain the Fourier cosine series for the given function over
the interval stipulated and sketch the function to which the series converges.
Interval, \(0
Problem 6
Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \text { Interval, }-c < x < c ; \text { function, } f(x)=x^{3} $$
Problem 6
In each exercise, obtain the Fourier cosine series for the given function over
the interval stipulated and sketch the function to which the series converges.
\(\begin{aligned} \text { Interval, } 0
Problem 7
In each exercise, obtain the Fourier cosine series for the given function over
the interval stipulated and sketch the function to which the series converges.
\(\begin{aligned} \text { Interval, } 0
Problem 7
Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \begin{aligned} \text { Interval, }-\pi< x < \pi ; \text { function, } f(x) &=3 \pi+2 x, &-\pi < x < 0, \\ &=\pi+2 x, & 0 < x < \pi \end{aligned} $$
Problem 7
In each exercise, obtain the Fourier sine series over the interval stipulated for the function given. Sketch the function that is the sum of the series obtained. Interval, \(0 < x < c ;\) function, \(f(x)=x(c-x)\).
Problem 8
In each exercise, obtain the Fourier sine series over the interval stipulated for the function given. Sketch the function that is the sum of the series obtained. Interval, \(0 < x < 2 ;\) function, \(\begin{aligned} f(x) &=x, & 0 < x < 1, \\\&=2-x, & 1 < x < 2 . \end{aligned}\)
Problem 8
In each exercise, obtain the Fourier cosine series for the given function over
the interval stipulated and sketch the function to which the series converges.
\(\begin{aligned} \text { Interval, } 0
Problem 8
Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \begin{aligned} \text { Interval, }-c < x < c ; \text { function, } f(x) &=x(c+x), &-c < x < 0, \\ &=(c-x)^{2}, & 0 < x < c . \end{aligned} $$
