# Thread: urgent help on limits

1. ## urgent help on limits

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

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:

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

RonL

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

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

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

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

6. I'm gonna go with galactus

7. 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

8. 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.

9. 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.

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

Thanks, PH, It actually worked.

11. if you are allowed use l'hopital rule

12. 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

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

14. 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?

15. 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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