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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

Hi, basic question here:

I have

lim 4z^2+z^6

_________

1-5z^3

x->positive infinity

Now, I know that this reduces to :

4/z+z^3

________= 0+infinity

_________

0-5

1/z^3 -5

which gives infinity over -5. Now, how do I evaluate infinity over a constant ??? Is there a fact or definition that tells us how to deal with this ?

Thank you

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

Hi;

The limit is of the form - ∞/∞ so you may use L'Hopitals rule on it.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

I didn't learn that... yet.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

Btw, if you want to see the problem, go her ; http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx

it's example 4 at the end

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

Have you tried to break the rational function into smaller pieces?

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**Maburo****Member**- From: Alberta, Canada
- Registered: 2013-01-08
- Posts: 287

L'Hopital's rule basically states that if

So you could differentiate the numerator and denominator until you no longer have 'z' in the denominator.

*Last edited by Maburo (2014-07-11 08:11:46)*

"Pure mathematics is, in its way, the poetry of logical ideas."

-Albert Einstein

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

I didn't learn differentiation...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

Divide the numerator and the denominator by z^3. Want to see how? You would then use:

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**Maburo****Member**- From: Alberta, Canada
- Registered: 2013-01-08
- Posts: 287

In the first post, that seems to have been done. Al-Allo reduced

"Pure mathematics is, in its way, the poetry of logical ideas."

-Albert Einstein

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

You are right, he is done then. - ∞ / 5 is -∞. That is the correct answer for the limit.

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**Maburo****Member**- From: Alberta, Canada
- Registered: 2013-01-08
- Posts: 287

Yes, indeed.

"Pure mathematics is, in its way, the poetry of logical ideas."

-Albert Einstein

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

But... how do you know that - ∞ / 5 is -∞ ???

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

http://www.vitutor.com/calculus/limits/ … inity.html

About half way down.

Also there is theorem about your original problem.

if the degree of z is higher on top, then the limit is infinity

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

Ah ok, thanks for the web page.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

Also, there is a theorem for when there is one polynomial over another. I put it into post #13.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

bobbym wrote:

Also, there is a theorem for when there is one polynomial over another. I put it into post #13.

Yes, I saw it

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

Are you satisfied or do you need anything else?

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

Well, I have another question.

If had something like

lim 9h

x->0

What do you do in these occasions ? Is there a definition that tells us the actions needed ? Thank you (I'm referring to the different letters.)

*Last edited by Al-Allo (2014-07-14 03:59:26)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

That would be 9h. Think about it, if x goes to 0 how does that affect 9h. It does not.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

bobbym wrote:

That would be 9h. Think about it, if x goes to 0 how does that affect 9h. It does not.

Well, at first i thought the same thing but wasn't too sure... ok thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,759

You could consider that 9h to be a constant and the limit operator does not affect it.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 324

Yeah, that would be an idea!

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