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09-15-2009 , 12:56 PM

PaulieWlnuts

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Join Date: Oct 2007 Posts: 2,054

I have an exam coming up and am stuck on a few problems.

This first one shows my poor algebra skills.

In the solution, I see that I'm supposed to multiply both the top and bottom of the fraction by

What's the purpose of this?

I'm especially confused about these last two steps. I think I'm forgetting something simple.

edit- hmmm the images aren't showing up correctly. not sure if I'm doing it right? its supposed to read lim as x approaches infinity and then the weird A^ got substituted for 3x squared etc. Fraction wouldn't show up either?

09-15-2009 , 01:25 PM

azoo

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Join Date: Feb 2009 Posts: 272

First of all we have to know where x tends to

09-15-2009 , 01:33 PM

PaulieWlnuts

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I'm not sure what you mean by tends to. The problem just says lim as x --> infinity. But I think I figured out why 1/x squared is used to multiply both sides.

It cancels out a lot of the garbage and leaves me with numbers that are zero save the 3 in the numerator and 1 in the denominator. I failed to realize the other numbers were just simply zero.

09-15-2009 , 01:42 PM

LongLiveYorke

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Join Date: May 2008 Posts: 527

Quote:

Originally Posted by PaulieWlnuts

Fixed it up a bit.

It should be clear that that square of a really big number is always bigger than the number itself. In other words, x*x is much greater than x as x goes to infinity. So, in the numerator, the 2x term and the 4 term become incredibly small compared to the 3x*x term. Similarly, the squared term in the denominator dominates the other terms. Therefore, we're only concerned with the fraction of the squared terms, which is 3. You'll get a good feel of what's going on if you plug in some numbers and see how quickly x*x grows much bigger than x.

09-15-2009 , 01:47 PM

PaulieWlnuts

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Join Date: Oct 2007 Posts: 2,054

I tried using the new image host. I just copy and pasted what I had from scientific notebook and placed in the correct spot. How'd you get it to work?

09-15-2009 , 01:48 PM

RosieTheGreat

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Join Date: Feb 2009 Posts: 2,192

Ill give you intuitive explanations for the first one... the second one is unreadable to me.

Also there is a hw questions thread. See: http://forumserver.twoplustwo.com/47...thread-581079/

Basically when you have these polynomial fraction ones that are tending to infinity, you only need to look at the highest degree terms, cause in the "long run" thats all that matters.

So basically you can rewrite the first problem as

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

09-15-2009 , 01:49 PM

LongLiveYorke

grinder

Join Date: May 2008 Posts: 527

Quote:

Originally Posted by PaulieWlnuts

I tried using the new image host. I just copy and pasted what I had from scientific notebook and placed in the correct spot. How'd you get it to work?

I edited the Latex code in your post. Quote this post to see what changes I made:

09-15-2009 , 01:58 PM

PaulieWlnuts

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Join Date: Oct 2007 Posts: 2,054

Ok, thanks guys/girl. Didn't see the homework thread. I'll use that even though this isn't homework. The less threads the better for stuff like this.

09-15-2009 , 10:01 PM

Bantam222

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Join Date: Aug 2006 Posts: 2,388

l'hospitals rule thing = do in head in like 2 sec.

09-15-2009 , 11:37 PM

#10

durkadurka33

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Join Date: Apr 2008 Posts: 8,709

Quote:

Originally Posted by Bantam222

l'hospitals rule thing = do in head in like 2 sec.

OMG I AGREE

Most 1st calc can be done in your head once you learn the tricks.

09-16-2009 , 12:51 AM

#11

PaulieWlnuts

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Join Date: Oct 2007 Posts: 2,054

We aren't allowed to use it. : (

09-16-2009 , 12:56 AM

#12

BruceZ

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Join Date: Sep 2002 Posts: 11,877

Quote:

Originally Posted by Bantam222
l'hospitals rule thing = do in head in like 2 sec.

OMG I AGREE

Most 1st calc can be done in your head once you learn the tricks.

Quote:

Originally Posted by PaulieWlnuts

We aren't allowed to use it. : (

Your head?

09-16-2009 , 11:15 AM

#13

LongLiveYorke

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Join Date: May 2008 Posts: 527

Quote:

Originally Posted by durkadurka33

OMG I AGREE

Most 1st calc can be done in your head once you learn the tricks.

The problem with Calculus is that there are so many "tricks" and techniques that often intuition and feel for the subject is lost. People get caught up in studying the formula for Integrating by Parts or whatever, but they don't really understand what an integral is.

09-16-2009 , 11:49 AM

#14

ac on

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Join Date: Jun 2009 Posts: 3,622

Quote:

Originally Posted by LongLiveYorke

I just remember how they got "tricks," personally. It sucks because I always have to work out the trick each time I want to use it, lol

E: Like in my calc II class, I can never remember the formulas for like, the volume of a function rotated around an axis, surface area, arc length, work, etc. I always have to sit and think about how it works.

I don't understand how the formulas for arc sin, arc cos, etc. were derived, so I'm probably going to fail the part of my test that has them, though.

09-16-2009 , 11:50 AM

#15

PaulieWlnuts

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Join Date: Oct 2007 Posts: 2,054

Quote:

Originally Posted by BruceZ

Your head?

Funny... What I meant was my professor doesn't care about the final solution, he grades us on how we arrived at the conclusion. He told those of us who knew how to solve the problem using l'hospital's rule need to put it out of our minds for now. He wants us to understand how everything works, not to just be able to memorize such and such formula and spit out such and such answer.

09-16-2009 , 12:26 PM

#16

FlyingPanda

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Join Date: Jul 2009 Posts: 171

so now you understand your problem?

09-16-2009 , 01:13 PM

#17

PaulieWlnuts

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Join Date: Oct 2007 Posts: 2,054

yeah close the thread please.

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