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Show that Sin | x | is continuous.

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  • 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 by thanvigandhi_1
 

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