The function $f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x 0 \end{array} \right\}$ has a Fourier series on $[ - 2,2 ]$ that converges at $x = 1$ to A) 7 B) 1 C) 1/2 D) $- 3$ E) unknown

Question

The function $f ( x ) = \left\{ \begin{array} { c c } 
x & \text { if } x < 0 \
2 + 5 x & \text { if } x > 0
\end{array} \right\}$ has a Fourier series on $[ - 2,2 ]$ that converges at $x = 1$ to
A) 7
B) 1
C) 1/2
D) $- 3$
E) unknown

Quizplus · Accepted Answer

The Fourier series of a function converges to the function's value at points where the function is continuous. At $x = 1$, the function $f(x) = 2 + 5x$, so $f(1) = 2 + 5(1) = 7$.

The Function f(x)={x if x<02+5x if x>0}f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x < 0 \\2 + 5 x & \text { if } x > 0\end{array} \right\}f(x)={x2+5x​ if x<0 if x>0​}

The Function $f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x < 0 \\2 + 5 x & \text { if } x > 0\end{array} \right\}$