Limit Problem

Date: 16 Jul 1995 02:59:45 -0400
From: Anonymous
Subject: Limits

From: Daniel Chavolla

Question: Could you please help me find this limit?

lim                x^2 + 2x
x --> infinity     -------     
                   5x - 5     

I know that the answer is 1/5, but how?                

Thanks.

Date: 17 Jul 1995 10:12:27 -0400
From: Dr. Ethan
Subject: Re: Limits

Hello Daniel,

Are you sure that the x isn't squared on the bottom?  Then the answer 
would be 1/5.  

I will show you how you could get 1/5 if the problem were slightly
different.

        If it was:   lim     x^2 + 2x
                             ---------
                   x-> inf   5x^2 -5

Do you know that we can multiply the top and bottom of a fraction by the
same thing and not change the value?  I hope so, because that is what we are
going to do.

We can multiply the top and bottom by 1/x^2 - then the fraction will look like

                           1 + 2/x
                           --------
                           5 - 5/x^2

So now we can take the limit of this.  2/x will go to zero and so will 5/x^2,
so all that is left is 1/5.  Did follow that?  If not then write back and I will try 
again.

Ethan Doctor On Call