Question

please solve it question.......​

Answer 1

Answer :

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)

Answer 2

Answer:

komal , plz refer pic above