Yay Limits!

[Qrrrbrbirbel]

lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

SOLVE ALGEBRAICALLY


<font size=-1>[ This Message was edited by: Qrrrbrbirbel on 2006-06-04 20:36 ]</font>

[Shattered_weasel]

No

[RicoRoyal]

On 2006-06-04 20:35, Qrrrbrbirbel wrote:
lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

SOLVE ALGEBRAICALLY


<font size=-1>[ This Message was edited by: Qrrrbrbirbel on 2006-06-04 20:36 ]</font>


Type 0/0

You can use L'Hospitals rule:

lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

= lim x-->1 {d/dx[(x^2 + x - 2)]}/{d/dx[(x - 1)]}

= lim x-->1 (2x + 1)/1

= (2*1 + 1)

= 3

[Dek]

On 2006-06-04 20:50, RicoRoyal wrote:


On 2006-06-04 20:35, Qrrrbrbirbel wrote:
lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

SOLVE ALGEBRAICALLY


<font size=-1>[ This Message was edited by: Qrrrbrbirbel on 2006-06-04 20:36 ]</font>


Type 0/0

You can use L'Hospitals rule:

lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

= lim x-->1 {d/dx[(x^2 + x - 2)]}/{d/dx[(x - 1)]}

= lim x-->1 (2x + 1)/1

= (2*1 + 1)

= 3



http://img.photobucket.com/albums/v607/arthas_zero/Misc/OWNED.png

[RicoRoyal]

On 2006-06-04 20:35, Qrrrbrbirbel wrote:
SOLVE ALGEBRAICALLY


Whooops. So much for following directions.

Ummm... you're on your own! *runs away*

Try asking astuarlen. Sorry.

[RicoRoyal]

I got it!

Multiply your function by (x - 1)/(x - 1), which is the same as multiplying by 1 (effectively changing nothing).

lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

= lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1) * [(x - 1)/(x - 1)]

= lim x-->1 ƒ(x)=(x^3 - 3x + 2)/(x - 1)^2

Factor the numerator and you get

lim x-->1 ƒ(x)=[(x + 2)*(x - 1)^2]/(x - 1)^2

The (x - 1)^2 in numerator and denominator cancel each other out.

Now you have...

lim x-->1 ƒ(x)=(x + 2)

= ƒ(1)=(1+2)

= 3

BOOM! HEADSHOT!

[HAYABUSA-FMW-]

On 2006-06-04 21:11, RicoRoyal wrote:
I got it!

= 3

BOOM! HEADSHOT!

HOT
http://capefeare.com/barthighheels.gif

[Qrrrbrbirbel]

On 2006-06-04 21:11, RicoRoyal wrote:
I got it!

Multiply your function by (x - 1)/(x - 1), which is the same as multiplying by 1 (effectively changing nothing).

lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1)

= lim x-->1 ƒ(x)=(x^2 + x - 2)/(x - 1) * [(x - 1)/(x - 1)]

= lim x-->1 ƒ(x)=(x^3 - 3x + 2)/(x - 1)^2

Factor the numerator and you get

lim x-->1 ƒ(x)=[(x + 2)*(x - 1)^2]/(x - 1)^2

The (x - 1)^2 in numerator and denominator cancel each other out.

Now you have...

lim x-->1 ƒ(x)=(x + 2)

= ƒ(1)=(1+2)

= 3

BOOM! HEADSHOT!




coulda just factored out the numerator ;*

[HAYABUSA-FMW-]

On 2006-06-04 21:17, Qrrrbrbirbel wrote:
coulda just factored out the numerator ;*


http://capefeare.com/homersale.gif

[Qrrrbrbirbel]

On 2006-06-04 21:18, HAYABUSA-FMW- wrote:


On 2006-06-04 21:17, Qrrrbrbirbel wrote:
coulda just factored out the numerator ;*


http://capefeare.com/homersale.gif



Don't make me bust out the Half-Angle Formulas

[RicoRoyal]

On 2006-06-04 21:17, Qrrrbrbirbel wrote:
coulda just factored out the numerator



-_- Wow, you're right. Guess that's what happens when one rushes into simple problems... just end up making them harder than necessary. Stupid, stupid, stupid! *hits self with trout* http://www.pso-world.com/images/phpbb/icons/smiles/icon_wet-trout.gif

In anycase, way to be an ass about it. http://www.pso-world.com/images/phpbb/icons/smiles/icon_disapprove.gif

[Qrrrbrbirbel]

I'm just glad that I can divide by zero now!

[RicoRoyal]

On 2006-06-04 21:57, Qrrrbrbirbel wrote:
I'm just glad that I can divide by zero now!



Congratulations.

lim x-->0 ƒ(x)=(tan(x) - x)/(x^3)

Go nuts.



<font size=-1>[ This Message was edited by: RicoRoyal on 2006-06-04 22:07 ]</font>

[Qrrrbrbirbel]

On 2006-06-04 22:07, RicoRoyal wrote:


On 2006-06-04 21:57, Qrrrbrbirbel wrote:
I'm just glad that I can divide by zero now!



Congratulations.

lim x-->0 ƒ(x)=(tan(x) - x)/(x^3)

Go nuts.




Not in Calculus yet, dunno how to do it, or else I would go nuts.

You're typing to the guy that memorized the Trigonomic Identities by writing them on the glass doors every time he took a shower >.<

[RicoRoyal]

On 2006-06-04 22:38, Qrrrbrbirbel wrote:
You're typing to the guy that memorized the Trigonomic Identities by writing them on the glass doors every time he took a shower >.<



http://www.pso-world.com/images/phpbb/icons/smiles/icon_lol.gif

Well, I 'spose if it works, stick with it! http://www.pso-world.com/images/phpbb/icons/smiles/icon_wacko.gif

In other news: *saves picture of bart in high heels*

[HAYABUSA-FMW-]

On 2006-06-04 22:42, RicoRoyal wrote:
In other news: *saves picture of bart in high heels*


This one too then,
http://capefeare.com/bart28.gif