Question

limits! help!

Answer 1

Do you know synthetic division?

Answer 2

Basically since \(3\) is a root for the numerator and denominator, that means you can factor out \(x-3\). So knowing polynomial division would help.

Answer 3

@mio long division?

Answer 4

Polynomial division.

Answer 5

i see, hm that would be easier.
my prof gave us this solution :
x^3-4x^2+9=x^3-3x^2+3x^2+x-30
i dont understand why he inserted +/-3x^2 there, have any idea?

Answer 6

That equation isn't true.

Answer 7

haha, it doesnt makes sense to me too but he ended up, getting (x-3)(x^2-x-3) by simplifying. the same goes to the denominator he also +/-3x^2 and got (x-3)(x^2+3x+10). then he sub to the limit. he got 3/28. i'll try the polynomial division thanks!(:

Answer 8

What I do is this: \[
\lim_{x\to 3}\frac{(x-3)(x^2-x-3)}{(x-3)(x^2+3x+10)}=\lim_{x\to 3}\frac{x^2-x-3}{x^2+3x+10}
\]

Answer 9

Then you can directly substitute.

Answer 10

^ my first reply was wrong it shd be, x^3-3x^2+3x^2-4x^2+9 my bad :p

Answer 11

Again, polynomial division will get you the factors.

Answer 12

yup! he also got the same, haha anw thanks polynomial division is easier for me!(:

Answer 13

What he did is what I call "magic factoring"

Answer 14

It is factoring that is done when you already know the result.

You expand the result out like when you multiply a polynomial...
THEN when it is time to demo to the students, you write down the expansion steps in reverse order.

No one has any idea how you came up with that. "magic factoring"

Answer 15

haha,i see..! now i kinda get it, but i'm not really good at my foundations so still makes me wonder sometimes. Anw, thanks for the help!(: its clear now haha *thumbs up*

Answer 16

For example: \[
\begin{split}
(a-b)(a+b)
&=a^2-ba+ab-b^2\\
&=a^2-b^2
\end{split}
\]Simple enough.

When you do in reverse order:\[
\begin{split}
a^2-b^2
&=a^2-ba+ab-b^2\\
&=(a-b)(a+b)
\end{split}
\]Hey, where did the \(-ba\) and \(ab\) come from?
What the hell?! Magic factoring.

Answer 17

Good luck.