please solve it question.......
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For all the x0>0 you have in a neighbourhood of x0 that |x|=x and you know f(x)=x is continuous over R. The same goes for x0<0. Then you only have to prove the continuity in 0. Considering that:
-limx→0−|x|=limx→0−−x=0
-limx→0+|x|=limx→0+x=0
you can conclude that
limx→0|x|=0
therefore the function is continuous in 0.
to prove that a function is continuous you just have to prove that it is continuous in every point (in fact, that's the definition)
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komal , plz refer pic above
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