Limit in driven harmonic oscillator function

Question

For a driven electric oscillator function we get the following amplitude function:

$$I_{max} (\Omega) = \frac{E}{\sqrt{R^2+\left(\Omega L-\frac{1}{\Omega C}\right)^{2}}}$$

where $E, R, L, C$ are some constants. How to prove that

$$\lim_{\Omega\rightarrow 0} I_{max} = 0 $$

With many thanks.

Answer 1

HINT:

Note that

$$\left|\frac{E}{\sqrt{R^2+\left(\Omega L-\frac1{\Omega C}\right)^2}}\right|\le \frac{|E|}{\left|\Omega L-\frac1{\Omega C}\right|}= \frac{|E||\Omega C|}{\left|\Omega^2LC-1\right|}$$