# Fourier Series/x over 0 to 2, x-2 over 2 to 4/Mistake

## Mistake

Find the half-range cosine series for
$f \left({x}\right) = \begin{cases} 1 & , 0 < x < 2 \\ x - 2 & , 2 < x < 4 \end{cases}$
for the half-range $0 < x < 4$.

The subsequent analysis is performed for the function:

$f \left({x}\right) = \begin{cases} x & : 0 < x \le 2 \\ x - 2 & : 2 < x < 4 \end{cases}$

and it is questionable whether it has actually been performed accurately.