Frequency response 1

The resistor with the capacitor are a voltage divider. Let's call $Z_c$ the capacitor's impedance and $R$ the resistor's impedance, we can calculate the voltage across the resistor as

$V_o = V_i \cdot \left(\frac{R}{R + Z_c}\right)$

We can calculate $Z_c$ in function of the frequency as $Z_c = \frac{-j}{2\pi f C}$ with $j = \sqrt{-1}$ . It's easy to see that the capacitor's impedance will get infinitely large as the frequency goes to zero, which means that $\left(\frac{R}{R + Z_c}\right)$ will get infinitesimally small and the voltage will go to zero.