# Show that Sin | x | is continuous.

Toolbox:
• Check whether $$LHL = RHL = f(a)$$ at any point $$x = a$$
LHL $$\lim\limits_{x \to \overline a}\: sin | x |$$
$$\lim\limits_{h \to 0} sin | a - h | = sin | a |$$
RHL = $$\lim\limits_{h \to 0} sin | a + h | = sin | a |$$
$$f(a) = sin | a |$$
$$\Rightarrow f$$ is continuous