urgent help on limits

**^_^Engineer_Adam^_^** · November 23rd 2006, 01:27 PM

45.)
$\lim_{x \to -1} \frac {2x^2-x- 3}{x^3+2x^2+6x+5} = ?$

**CaptainBlack** · November 23rd 2006, 01:37 PM

Originally Posted by ^_^Engineer_Adam^_^

45.)
$\lim_{x \to 1} \frac {2x^2-x- 3}{x^3+2x^2+6x+5} = ?$

Because both the numerator and denominator are well behaved at $x=1$ the limit may be evaluated by substituting $1$ for $x$ so:

$<br /> \lim_{x \to 1} \frac {2x^2-x- 3}{x^3+2x^2+6x+5} = \frac{-2}{14}=-\frac{1}{7}<br />$

RonL

**^_^Engineer_Adam^_^** · November 23rd 2006, 01:49 PM

sorry for my mistake 45 is $\lim_{x \to -1}$
thank u very much!

**topsquark** · November 23rd 2006, 03:57 PM

Originally Posted by ^_^Engineer_Adam^_^

45.)
$\lim_{x \to -1} \frac {2x^2-x- 3}{x^3+2x^2+6x+5} = ?$

In this case both the numerator and denominator are 0. Thus we may use L'Hopital's rule:

$\lim_{x \to -1} \frac {2x^2-x- 3}{x^3+2x^2+6x+5} = \lim_{x \to -1} \frac {4x - 1}{3x^2 + 4x + 6} = \frac{3}{5}$

-Dan

**galactus** · November 23rd 2006, 04:59 PM

$\lim_{x\to\-1}\frac{2x^{2}-x-3}{x^{3}+2x^{2}+6x+5}=\lim_{x\to\-1}\frac{(x+1)(2x-3)}{(x+1)(x^{2}+x+5)}=\lim_{x\to\-1}\frac{2x-3}{x^{2}+x+5}=-1$

That supoosed to be a -1 under the limit symbol, but for some reason it won't display.

**Ranger SVO** · November 23rd 2006, 05:48 PM

I'm gonna go with galactus

**topsquark** · November 24th 2006, 04:23 AM

Originally Posted by topsquark

In this case both the numerator and denominator are 0. Thus we may use L'Hopital's rule:

$\lim_{x \to -1} \frac {2x^2-x- 3}{x^3+2x^2+6x+5} = \lim_{x \to -1} \frac {4x - 1}{3x^2 + 4x + 6} = \frac{3}{5}$

-Dan

You know, you'll get MY answer if you put x = 1 in the numerator and x = -1 in the denominator...

-Dan

**galactus** · November 24th 2006, 07:25 AM

Originally Posted by Ranger SVO

I'm gonna go with galactus

Hello Ranger SVO.

May I ask, if it's not too much trouble, how you managed to post the screen from your Voyage 200?. I have a TI-92 with the GraphLink; I have my programs backed up and so forth, but I've not done that. I know if I try, I'll probably get some annoying error message.

**ThePerfectHacker** · November 24th 2006, 07:40 AM

Originally Posted by galactus

Hello Ranger SVO.

May I ask, if it's not too much trouble, how you managed to post the screen from your Voyage 200?. I have a TI-92 with the GraphLink; I have my programs backed up and so forth, but I've not done that. I know if I try, I'll probably get some annoying error message.

I am guessing he has a cable that attaches to a computer. Then it displays on the screen. He took a screenshot.

**galactus** · November 24th 2006, 07:43 AM

Oh, O.K., PH. I'll try that.

Thanks, PH, It actually worked.

**oahsen** · November 24th 2006, 07:54 AM

if you are allowed use l'hopital rule

**Ranger SVO** · November 24th 2006, 08:33 AM

Originally Posted by galactus

Hello Ranger SVO.

May I ask, if it's not too much trouble, how you managed to post the screen from your Voyage 200?. I have a TI-92 with the GraphLink; I have my programs backed up and so forth, but I've not done that. I know if I try, I'll probably get some annoying error message.

TI Connect has a screen capture button, right next to Device Explorer.
Right after you press, screen capture, in the tool bar is a copy button.
I'll bet you got it from there

**galactus** · November 24th 2006, 08:43 AM

That's what I done Ranger. I was glad it worked so slick.

**Ranger SVO** · November 24th 2006, 08:57 AM

Originally Posted by galactus

That's what I done Ranger. I was glad it worked so slick.

I wonder if I have Greens Theorum on mine, I'll have to look now. I don't remember seeing it. Did you find that somewhere?

**galactus** · November 24th 2006, 09:07 AM

That's a program I wrote a long time ago. I was playing with it at the time I used the screen capture.

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