«

[Kon-Tiki]

Fifth exercise, in the solution, how did they get -6? In my eyes, logically, the outcome'd be non-existing, due to division by 0.

[Havell]

This is calculus, that means the thing you should be interested in is the value of the function as x approachs 9, not when it equals 9 so the denominator will get very small but should not quite be 0.

[Kon-Tiki]

How do they get -6 then instead of 0? Or in this case, very close to -6 instead of very close to 0?

Also, how'd they get rid of the bottom part of the division in the next to one last exercise?

[xoopx]

OW MY BRAIN

[Havell]

In the next to last question, they canceled the denominator with the expanded (x-4) cubed to get (x-4)|x-4| which tends towards 0.

[Fawfulhasfury]

How does (x-4) cubed lead to 0

[Kon-Tiki]

Found what they did in both. Seems that they did this:
9-x = (sqrt(x)+3)(-sqrt(x)+3)
And x-9 = (sqrt(x)+3)(sqrt(x)-3)
So they can scratch (sqrt(x)+3), leaving
(-sqrt(x)+3) <blablabla> / (sqrt(x)-3).
Then they put the top - outside of the brackets, giving this:
-(sqrt(x)-3) <blablabla> / (sqrt(x)-3)
You can now scratch (sqrt(x)-3), leaving:
-<blablabla>.
In the 5th exercise, it ends up beautifully in -6. In the next-to-last one, it ends up in
|x-4|?
I haven't fully figured out why they tossed one out in front, so that it looks like
(x-4)|x-4|

Thanks goes to Pogo on another forum for pointing the sqrt(x) thingy out.

[Borodin]

Originally posted by xoopx@Jan 15 2005, 12:30 AM
OW MY BRAIN

Amen to that, brother. Whenever I hear this kind of discussion my eyes glaze over and I begin searching for a Klien bottle to jump into.

[Kon-Tiki]

Meh, just a matter of not thinking "I don't understand this" on first sight, but try to follow the reasoning. That's how I'm improving on it, and I suck at math k:

[Borodin]

Originally posted by Kon-Tiki@Jan 15 2005, 03:59 AM
Meh, just a matter of not thinking "I don't understand this" on first sight, but try to follow the reasoning. That's how I'm improving on it, and I suck at math k:

On first sight? I've been trying to learn higher math probably for more years than you've been living, simply because I *felt* I should. I even asked my wife to explain algebra, which I took a year of back in high school long ago. Of course, she's a math head; but although she tried diligently, it didn't work. Give me words, colors, sounds; even give me the logic behind words. But I prefer the emotion behind logic.