There are some things wrong in the following demonstration. Find the mistakes and correc...

There are some things wrong in the following demonstration. Find the mistakes and correct them.

In this exercise we attempt to obtain the Fourier cosine coefficients of e^x:

Since Equations (3.4.22) and (3.4.23) give the Fourier cosine series of ex, they must be identical. Thus,

By correcting the mistakes, you should be able to obtain A₀ and A_n without using the typical technique, that is,