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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.
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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