Chapter 7.13, Problem 9MP

Given $f(x)=$ $\{$ $x,0<x<1$, $-2,1<x<2$.

(a) Sketch at least three periods of the graph of the function represented by the sine series for $f(x).$ Without finding any series, answer the following questions: (b) To what value does the sine series in (a) converge at $x=1?$ At $x=2?$ At $x=0?$ At $x=-1?$

(c) \quad$ If the given function is continued with period 2 and then is represented by a complex exponential series ${\displaystyle \underset{n=-\infty }{\overset{\infty }{\sum }}{c}_n}{e}^{in\pi x},$ what is the value of