Fourier of Half-Wave Rectified

1. Feb 14, 2013

izen

1. The problem statement, all variables and given/known data

How did $\frac{1}{2}x$ come from at k=1?

2. Relevant equations

3. The attempt at a solution

because k=1 will make the first term at denominator 2(k-1) = $\frac{0}{0}$

2. Feb 14, 2013

SammyS

Staff Emeritus
Yes. The $\ \frac{1}{2}x\$ comes from the fact that the first term has the form 0/0 as k → 1.

What is $\displaystyle \ \lim_{t\to0}\frac{\sin(t)}{t}\ ?$

3. Feb 14, 2013

izen

Use L' Hopital's Rule --> $\displaystyle \ \lim_{t\to0}cos(t) = 1$

thank you SammyS