Evaluating Limits

Evaluate lim x/((x+2)^2 - 4) as x-> 0 or state that the limit does not exist.

My book said I can substitute 0 into the equation. I did that and came up with
____0_____
(0+2)^2 -4 which simplifies down to

___0___ which = _0_ which = _0_ = 0.
2^2 - 4 4-4 0

That's indeterminate, so I did it another way and factored out (x+2)^2 first. This is what I got:

_____x____ = ___x___
x^2+4x+4-4 x^2 + 4

And then I substituted 0 to get:

___0____ = _0_ = _0_ = 0.
0^2 +4*0 0+0 0

I'd like to know; is 0 my limit, or does a result of 0 determine that no limit exists? My book is not clear on this. Please let me know!

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asked by Tabby
  1. _x_________ =
    x^2+4x+4-4

    = ___x____
    X^2 + 4 x

    = ____x____
    x(x+4)

    = _____1____
    (x+4)

    which is 1/4 when x = 0

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    posted by Damon
  2. Oh....That would make more sense. Thanks for explaining that!

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    posted by Tabby

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