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Math Help - Very stupid continuity question

  1. #1
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    Very stupid continuity question

    Is the function (x^2 - 4)/(x + 2) continous at x=-2 ?

    I am doubtful because
    1. It can be reduced to (X-2) so it is continous everywhere.
    2. But on the other hand isnt continuity checked for the exact function without making changes to it? Cos if x=-2 then the original function is not defined at all.
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  2. #2
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    \frac{(x^2 - 4)}{(x + 2)} = \frac{(x+2) (x-2) }{(x + 2)}
    It is not continuous at x = -2. There is a hole there
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  3. #3
    Junior Member woof's Avatar
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    Quote Originally Posted by champrock View Post
    .....if x=-2 then the original function is not defined at all.
    And that is the reason why the function is not cts at x=-2.

    For continuity, the behavior at the point must agree with the behavior near the point. Approaching x=-2, you get a limit. At the point, the function is not even defined. Thus the hole, as mentioned above.
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