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Magazine Problem 1
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 1
In Exercises 1 through 22, obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$\begin{aligned}\text { Interval, }-c < x < c ; \text { function, } f(x) &=0, &-c < x < 0, \\\&=c-x, & 0 < x < c .\end{aligned}$$
Problem 1
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, \(f(x)=1\)
Problem 2
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 2
Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \text { Interval, }-c < x < c ; \text { function, } f(x)=x $$
Problem 3
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, \(f(x)=x^{2} .\) Check your answer with that for the example in the text above.
Problem 3
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 4
Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \begin{aligned} \text { Interval, }-c < x < c ; \text { function, } f(x) &=0, &-c < x < 0, \\ &=(c-x)^{2}, & 0 < x < c . \end{aligned} $$
Problem 4
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 4
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, \(f(x)=c-x\)
