Find $a_{0}$ for the function $f(x)=$$\left\{\begin{array}{c}
-1 \
1
\end{array}\right.$$\begin{array}{c}
-\pi

Question

Find $a_{0}$ for the function $f(x)=$$\left\{\begin{array}{c}
-1 \
1
\end{array}\right.$$\begin{array}{c}
-\pi< \
0<
\end{array}$$\begin{array}{l}
x \leq 0 \
x \leq \pi
\end{array}$
 .
A)1
B)-1
C)1/2
D)-1/2
E)0

Quizplus · Accepted Answer

$a_{0}$ is the average value of the function over one period. For the given function, the average value is $0$ because the function takes on values of $1$ and $-1$ over equal intervals, thus averaging to $0$.

Find a0a_{0}a0​ For the Function f(x)=f(x)=f(x)= {−11\left\{\begin{array}{c}-1 \\1\end{array}\right.{−11​ −π<0<\begin{array}{c}-\pi< \\0<\end{array}−π<0<​ x≤0x≤π\begin{array}{l}x \leq 0 \\x \leq \pi\end{array}x≤0x≤π​

Find $a_{0}$ For the Function $f(x)=$ $\left\{\begin{array}{c}-1 \\1\end{array}\right.$ $\begin{array}{c}-\pi< \\0<\end{array}$ $\begin{array}{l}x \leq 0 \\x \leq \pi\end{array}$