Looking at:
$|H|={1 \over {\sqrt{1+(\omega RC)^2}}}$
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As $\omega \rightarrow 0$:

$$|H| \rightarrow {1 \over {\sqrt{1+(0 RC)^2}}} = {1\over 1} = 1$$

As $\omega \rightarrow \infty$:

$$|H| \rightarrow {1 \over {\sqrt{1+(\infty RC)^2}}} = {1\over \infty} = 0$$