       Re: What is this doing...?...

• To: mathgroup at smc.vnet.net
• Subject: [mg14790] Re: [mg14766] What is this doing...?...
• From: Jurgen Tischer <jtischer at col2.telecom.com.co>
• Date: Wed, 18 Nov 1998 01:28:53 -0500
• References: <199811140807.DAA03449@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```What is it doing..., Mitch?
It shows you what happens if you approximate a function with its Taylor
series beyond its radius of convergence. If you plot for 26 you will
see there's nothing magic about 30, it's just that the highest power
dominates, so it goes up for even and down for odd powers. By the way,
at the other end it goes always down, because your highest power always
enters with a minus.

Jurgen

>
> I've having some trouble interpreting a graph I receive in mathematica,
> maybe someone can help?  Here's what I have:
>
> Normal[Series[Sin[x], {x,0,#}]]& /@ {1,3,5,7}
> f[#]& /@ {arg1, arg2, arg3}
> Join[{a,b,c}, {d,e}]
> plotts[fx_, a0_: 0, {x_,a_,b_}, k_List, opt___]
> :=Plot[Evaluate[Join[Normal[Series[fx,{x,a0,#}]]& /@ k, {fx}]], {x,a,b},
> opt]
>
> now I type the command to graph:
>
> plotts[Log[x+1], {x, -.99,2}, {1,3,25}, PlotRange->{-5,2}]
>
> and all is well however when I change the 25 to 30 I get a different
> graph, why?  What is going on here?  I believe this is a Taylor series
> or something, but can someone explain to me when I change the
> plotts[Log[x+1], {x, -.99,2}, {1,3,25}, PlotRange->{-5,2}] to
> plotts[Log[x+1], {x, -.99,2}, {1,3,30}, PlotRange->{-5,2}] I get a
> different graph?  I must admit I've only used mathematica for about 15
> minutes...so an explanation as to why this graph is changing would
> really help.
>
> Thanks,
>
> --