Let $g(x)=\begin{cases} 5 x, & 0 < x < 3.5 \cr 13-x, & 3.5 \leq x < 7 \cr \end{cases}$.

Let $S(x)$ be the Fourier Sine series of $g$.

$S(x)= \displaystyle\sum_{n=1}^{\infty}\Bigg[\Big($ $\displaystyle\Big)\sin\Big(\frac{n \pi}{7}x\Big)\Bigg]$

What does $S(-7)$ equal?$\ \ \ \ S(-7)=$

What does $S(-5.25)$ equal?$\ \ \ \ S(-5.25)=$

What does $S(-3.5)$ equal?$\ \ \ \ S(-3.5)=$

What does $S(-1.75)$ equal?$\ \ \ \ S(-1.75)=$

What does $S(0)$ equal?$\ \ \ \ S(0)=$

What does $S(1.75)$ equal?$\ \ \ \ S(1.75)=$

What does $S(3.5)$ equal?$\ \ \ \ S(3.5)=$

What does $S(5.25)$ equal?$\ \ \ \ S(5.25)=$

What does $S(7)$ equal?$\ \ \ \ S(7)=$

Let $C(x)$ be the Fourier Cosine series of $g$.

$C(x)=$ $+ \displaystyle\sum_{n=1}^{\infty}\Bigg[ \Big($ $\displaystyle\Big)\cos\Big(\frac{n \pi}{7}x\Big) \Bigg]$

What does $C(-7)$ equal?$\ \ \ \ C(-7)=$

What does $C(-5.25)$ equal?$\ \ \ \ C(-5.25)=$

What does $C(-3.5)$ equal?$\ \ \ \ C(-3.5)=$

What does $C(-1.75)$ equal?$\ \ \ \ C(-1.75)=$

What does $C(0)$ equal?$\ \ \ \ C(0)=$

What does $C(1.75)$ equal?$\ \ \ \ C(1.75)=$

What does $C(3.5)$ equal?$\ \ \ \ C(3.5)=$

What does $C(5.25)$ equal?$\ \ \ \ C(5.25)=$

What does $C(7)$ equal?$\ \ \ \ C(7)=$

Let $f(x)$ be the Fourier series of $g$ if $g$ is extended to$(-7,0)$ so that $g(x)=g(x+7)$.

$f(x)=$ $+\displaystyle\sum_{n=1}^{\infty} \Bigg[ \Big($ $\displaystyle\Big)\cos\Big(\frac{2 n \pi}{7}x\Big) + \Big($$\displaystyle\Big)\sin\Big(\frac{2 n \pi}{7}x\Big) \Bigg]$

What does $f(-7)$ equal?$\ \ \ \ f(-7)=$

What does $f(-5.25)$ equal?$\ \ \ \ f(-5.25)=$

What does $f(-3.5)$ equal?$\ \ \ \ f(-3.5)=$

What does $f(-1.75)$ equal?$\ \ \ \ f(-1.75)=$

What does $f(0)$ equal?$\ \ \ \ f(0)=$

What does $f(1.75)$ equal?$\ \ \ \ f(1.75)=$

What does $f(3.5)$ equal?$\ \ \ \ f(3.5)=$

What does $f(5.25)$ equal?$\ \ \ \ f(5.25)=$

What does $f(7)$ equal?$\ \ \ \ f(7)=$