Find the limit of a? as the limit approaches infinity and b) as the limit approaches negative infinity of (3X^2-6X)/(4X-8). I understand that the answer has to be infinity and negative infinity. But can someone explain to me why mathematically it works out?
2006-09-16 02:14:08 · 4 answers · asked by Aurora 1 in Science & Mathematics ➔ Mathematics
OKay, factor out first:
(3x^2-6x)/(4x-8) = ((3x(x-2))/(4(x-2))).
So, the (x-2) cancels out, giving you (3x)/4.
So, now I think you can see how it goes to infinity and negative infinity.
2006-09-16 02:21:38 · answer #1 · answered by yljacktt 5 · 0⤊ 0⤋
well the term 3x^2 dominates all the other infinities, meaning that it increases at a far greater rate than 6x or 4x and will cancel out the effect of those terms.
Effectively making the numerator a huge infinity and the numerator either a positve or negative infinity depending on if you take the limit of a or b. The huge infinity gobbles up the attempt of the smaller infinity to drag it down to a rational number.
That's the best way I can explain it. I haven't used limit's in several years so I don't remember how to mathematically prove it. Not sure if this was the type of explaination you were looking for or not.
Hmm..., the guy above makes it much easier lol
2006-09-16 09:29:23 · answer #2 · answered by Justaguyinaplace 4 · 0⤊ 0⤋
If you're having trouble with this, maybe Calculus was a bad choice. It's only going to get harder from here on out. The limit stuff they teach you in the first couple of chapters is only a primer.
Good luck.
2006-09-16 10:13:25 · answer #3 · answered by WildPointer 3 · 0⤊ 0⤋
You find it
2006-09-16 09:16:58 · answer #4 · answered by Anonymous · 0⤊ 0⤋