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Continuity And Differentiability

Question
CBSEENMA12034565
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Discuss the continuity of the following functions :
f(x) = sin x.cos x

Solution

f(x) = sin x cos.x
Df = R
Let a be any real number.
space Lt with straight x rightwards arrow straight a below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow straight a below left parenthesis sin space straight x space cos space straight x right parenthesis equals sin space straight a space cos space straight a Also space straight f left parenthesis straight a right parenthesis equals sin space straight a space cos space straight a therefore space Lt with straight x rightwards arrow straight a below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight a right parenthesis therefore space straight f space is space continuous space at space straight x equals straight a But space straight a space is space any space point space of space straight R. space space therefore space straight f space is space continuous space function.

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