Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Limits at infinity

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

Hi;

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

I didn't learn that...  yet.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Maburo

Member

From: Alberta, Canada

Registered: 2013-01-08

Posts: 287

Re: Limits at infinity

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)

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

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

I didn't learn differentiation...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Maburo

Member

From: Alberta, Canada

Registered: 2013-01-08

Posts: 287

Re: Limits at infinity

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Maburo

Member

From: Alberta, Canada

Registered: 2013-01-08

Posts: 287

Re: Limits at infinity

Yes, indeed.

---

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

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

Ah ok, thanks for the web page.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

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

Yes, I saw it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

Are you satisfied or do you need anything else?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

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)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits at infinity

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Limits at infinity

Yeah, that would be an idea!