Re: Re:"Limit involving square root"

*To*: mathgroup at smc.vnet.net*Subject*: [mg30253] Re: [mg30235] Re:"Limit involving square root"*From*: George Woodrow III <georgevw3 at mac.com>*Date*: Sat, 4 Aug 2001 01:14:22 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I tried plotting the original function from 0 to 10^16, and got a lot of artifacts. There is a strong horizontal line at 5, and spikes. What you got were probably artifacts. If you rewrite the function as x - Sqrt[(x - 9) (x - 1)], it should be clear that as x approaches infinity, this approximates x - Sqrt[x^2] = 0. Don't know why Mathematica is confused. Nlimit[] reports 5 for as the limit and 6 for the function + 1. george On Friday, August 3, 2001, at 12:56 am, Zakir F. Seidov wrote: > In my case also > Series is OK, but Limit is NOT: > > In[1]:=$Version > Out[1]="4.0 for Microsoft Windows (December 5, 1999)" > > In[2]:=Limit[x - Sqrt[9 - 10 x + x^2], x -> Infinity] > Out[2]=5 > > In[3]:=Limit[a + x - Sqrt[9 - 10 x + x^2], x -> Infinity] > Out[3]=a > > In[4]:= > Normal[Series[a + x - Sqrt[9 - 10 x + x^2], {x , Infinity, 4}] ] > > Out[4]= > 5 + a + 232/x^3 + 40/x^2 + 8/x > > What a suprise for us users?! > Zakir > """"""""""""""""""""""""" > """"""""""""""""""""""""" > Subject: [mg30253] [mg30235] Limit involving square root > Author: Hugh Goyder <goyder at rmcs.cranfield.ac.uk> > Organization: Steven M. Christensen and Associates, Inc and > MathTensor, Inc. > > Dear Mathgroup, > > Below I take the limit of a function and then the limit of 1 plus the > same > function. A plot of the function shows that the first result, (5), is > correct but the second, (1), is wrong. (Should be 6.) What's > happening? > > In[1]:=$Version > > Out[1]= > 4.1 for Microsoft Windows (November 2, 2000) > > In[2]:= > Limit[x - Sqrt[9 - 10 x + x^2],x -> Infinity] > > Out[2]=5 > > In[3]:= > Limit[1 + x - Sqrt[9 - 10 x + x^2],x -> Infinity] > > Out[3]=1 > > I also note that using Series to expand about infinity does give the > correct answers. > > Thanks > > Hugh Goyder > > >