91Ó°ÊÓ

In each exercise, obtain the Fourier cosine series for the given function over the stipulated interval and sketch the function to which the series converges. \(\begin{aligned} \text { Interval, } 0< x< 2 ; \text { function, } f(x) &=x, & 0< x<1, \\ &=2-x, & 1< x< 2 \end{aligned}\)

In each exercise, obtain the Fourier sine series over the stipulated interval for the function given. Sketch the function that is the sum of the series obtained. Interval, \(0

Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \begin{aligned} \text { Interval, }-c< x< c ; \text { function, } f(x) &=0, &-c< x< 0 \\ &=c-x, & 0< x< c \end{aligned} $$

In each exercise, obtain the Fourier cosine series for the given function over the stipulated interval and sketch the function to which the series converges. $$ \begin{aligned} \text { Interval, } 0< t< t_{1} ; \text { function, } f(t) &=1, & 0< t< t_{0} \\\ &=0, & t_{0}< t< t_{1} \end{aligned} $$

In each exercise, obtain the Fourier cosine series for the given function over the stipulated interval and sketch the function to which the series converges. Interval, \(0< x< 1 ;\) function, \(f(x)=(x-1)^{2}\)

In each exercise, obtain the Fourier cosine series for the given function over the stipulated interval and sketch the function to which the series converges. Interval, \(0< x< c ;\) function, \(f(x)=x(c-x)\)

In each exercise, obtain the Fourier sine series over the stipulated interval for the function given. Sketch the function that is the sum of the series obtained. Interval, \(0

Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \begin{aligned} \text { Interval, }-c< x< c ; \text { function, } f(x) &=0, &-c< x< 0 \\ &=(c-x)^{2}, & 0< x< c \end{aligned} $$

Obtain the Fourier series over the indicated interval for the given function. Always sketch the function that is the sum of the series obtained. $$ \begin{aligned} \text { Interval, }-c< x< c ; \text { function, } f(x) &=0, &-c< x< 0 \\ &=1, & 0< x< c \end{aligned} $$

In each exercise, obtain the Fourier cosine series for the given function over the stipulated interval and sketch the function to which the series converges. Interval, \(0< x< c ;\) function, \(f(x)=c-x\)