Let $g(x)=7 x^2 + 19 x$ for $0 < x < 11$.

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

$S(x)= \displaystyle\sum_{n=1}^{\infty}\Bigg[\Big($ $\displaystyle\Big)\sin\Big(\frac{n \pi}{11}x\Big)\Bigg]$

What does $S(-11)$ equal?$\ \ \ \ S(-11)=$

What does $S(-8.25)$ equal?$\ \ \ \ S(-8.25)=$

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

What does $S(5.5)$ equal?$\ \ \ \ S(5.5)=$

What does $S(11)$ equal?$\ \ \ \ S(11)=$

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

$C(x)=$ $+ \displaystyle\sum_{n=1}^{\infty}\Bigg[ \Big($ $\displaystyle\Big)\cos\Big(\frac{n \pi}{11}x\Big) \Bigg]$

What does $C(-11)$ equal?$\ \ \ \ C(-11)=$

What does $C(-8.25)$ equal?$\ \ \ \ C(-8.25)=$

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

What does $C(5.5)$ equal?$\ \ \ \ C(5.5)=$

What does $C(11)$ equal?$\ \ \ \ C(11)=$

Let $f(x)$ be the Fourier series of $g$ if $g$ is extended to$(-11,0)$ so that $g(x)=g(x+11)$.

$f(x)=$ $+\displaystyle\sum_{n=1}^{\infty} \Bigg[ \Big($ $\displaystyle\Big)\cos\Big(\frac{2 n \pi}{11}x\Big) + \Big($$\displaystyle\Big)\sin\Big(\frac{2 n \pi}{11}x\Big) \Bigg]$

What does $f(-11)$ equal?$\ \ \ \ f(-11)=$

What does $f(-8.25)$ equal?$\ \ \ \ f(-8.25)=$

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

What does $f(5.5)$ equal?$\ \ \ \ f(5.5)=$

What does $f(11)$ equal?$\ \ \ \ f(11)=$

You can earn partial credit on this problem.