Asked by Tabby
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!
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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