# Fourier of Half-Wave Rectified

## Homework Statement

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

## The Attempt at a Solution

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

SammyS
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## Homework Statement

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

## The Attempt at a Solution

because k=1 will make the first term at denominator 2(k-1) = $\frac{0}{0}$
Yes. The $\ \frac{1}{2}x\$ comes from the fact that the first term has the form 0/0 as k → 1.

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

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

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

thank you SammyS