Math, asked by gagan54, 1 year ago

please explain this solution

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Answered by kvnmurty
1
Well, it is a question and answer on the limits and continuity topic.

The function f(x) is defined in two separate domains. It is not defined at f(0). So it is not continuous at x=0.

f(x) = x + 2   if x < 0
     = - x + 2   if x > 0

Actually it is like   f(x) = 2 - | x |   ∀ x  except for x = 0.
                                 = undefined for x= 0.

It is needed to prove that  Limit as x → c,  f(x) = f(c) always.  
This is true in both domains D1 for x < 0 and for domain D2 for x > 0.

That is all. We know  x+@ and -x +2 are continuous straight lines. Easy to prove that.

kvnmurty: :-)
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