Re: Limit[f[x], x->a] vs. f[a]. When are they equal?
- To: mathgroup at smc.vnet.net
- Subject: [mg118374] Re: Limit[f[x], x->a] vs. f[a]. When are they equal?
- From: Richard Fateman <fateman at eecs.berkeley.edu>
- Date: Mon, 25 Apr 2011 07:27:27 -0400 (EDT)
On 4/24/2011 4:57 PM, Richard Fateman wrote:
> ...
>
> First, a bug?
>
> Series[1/(1-Exp[I x]), {x, 0, 4}] returns unevaluated. A bug?
I tried this again. Somehow I managed to insert the denominator as a
TextCell, and didn't notice it.
Maybe I cut/pasted from the wrong place. Anyway, I checked and saw the
InputForm
TextCell["(1-Exp[I x])"]^(-1)
Sorry.
<snip>
But now try this:
s= 1/(1-Exp[I x])
Limit[s,x->0] gives ComplexInfinity
but
Limit [Series[s,{x,0,4}],x->0 gives I * Infinity.
Can these both be right?
but then, Sin[2*x] = 2*Cos[x]*Sin[x], ... yet Limit[ ..,x->Infinity]
gives 2 different answers. oh well.
RJF