Originally Posted by
Sneaky i got to the step
-3x (1/-x)
-------------------------
(x- sqrt(x^2 + 3x))(1/-x)
then for the numerator i simplify and get 3
but for the bottum part i dont see how you get -2
and why does 3/x = 0, why do you assume that?
Oh, dear god: who ever wrote such a nonsense?! I said 3/x --> 0, not equality! Meaning, of course, that x--> oo or x --> -oo, it's the same in both cases.
Now the denominator:
(x- sqrt(x^2 + 3x))(1/-x) = x*(-1/x) - (-1/x)Sqrt(x^2 + 3x) =
-1 - Sqrt([x^2 + 3x]/x^2) = -1 - Sqrt(1 + 3/x)
Rememebr that if a is a non-negative real number, the a*Sqrt(h) = Sqrt(ah) , and this is why we needed -1/x = 1/-x and NOT 1/x, because since
we're taking the limit as x --> -oo we're going to work with NEGATIVE x's, so in order to get somethinbg into a square root we took -1/x, which is POSITIVE (as 1/x is negative!).
Tonio
Pd. Read carefully this and my prior answers, work on them with pencil and paper, THINK...and after a good while of honest effort, if you don't succeed then write back.
why does
-sqrt(x^2 + 3x)
---------------- = -1 ?
-x