Let f(x)=1 |x - 1| be a function defined on (0, 2). (a) Find the even...

 

Transcribed Image Text:

Let f(x)=1 |x - 1| be a function defined on (0, 2). (a) Find the even and odd periodic extensions of f, and sketch their graphs with at least three periods. (b) Find the Fourier series for both the even and odd extensions. (c) Find the exact value of 1 - 1 32 1 - + + 1 72 92 - 1 112 (HINT: evaluate your Fourier series at a suitable point) - 132 1 1 + 152 172 Let f(x)=1 |x - 1| be a function defined on (0, 2). (a) Find the even and odd periodic extensions of f, and sketch their graphs with at least three periods. (b) Find the Fourier series for both the even and odd extensions. (c) Find the exact value of 1 - 1 32 1 - + + 1 72 92 - 1 112 (HINT: evaluate your Fourier series at a suitable point) - 132 1 1 + 152 172