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# Show that Sin | x | is continuous.

Can you answer this question?

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
answered Mar 11, 2013