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Show that the function $f(x) = | \sin x+\cos x| $ is continuous at $ x =\Large\pi$

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  • For continuous at $ x = \pi, LHL = RHL = f(\pi)$
$ LHL\: \lim\limits_{h \to 0} \: | sin(\pi-h)+cos(\pi-h)|$
$ LHL\: \lim\limits_{h \to 0} \: | sin\: h-cos\:h | = 1$
RHL $ LHL\: \lim\limits_{h \to 0} \: | sin(\pi+h)+cos(\pi+h)|$
= $ \lim\limits_{h \to 0} \: | -sin\:h-cos\: h | = 1$
$ f(\pi) = | sin\pi+ cos\pi | = 1$
$ \Rightarrow f$ is continuous at $ x = \pi$

 

answered Mar 11, 2013 by thanvigandhi_1
edited Mar 26, 2013 by thanvigandhi_1
 

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