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From: "Richard Fateman" <fateman at cs.berkeley.edu>
Sent: Thursday, September 09, 2010 10:12 AM
To: "Dan" <vi5u0-maxima at yahoo.co.uk>
Cc: "Maxima mailing list" <maxima at math.utexas.edu>
Subject: Re: [Maxima] RE : inf - inf = 0 ??
> On 9/9/2010 3:46 AM, Dan wrote:
>> On Wed, 8 Sep 2010, Richard Hennessy wrote:
>>
>>> Yes, it does mean that. limit(expr1,x,a)-limit(expr2,x,a) is not always equal to limit(expr1-expr2,x,a);
>>
>> According to my notes on Erd?lyi (1956, _Asymptotic expansions_, Dover
>> Publications, New York, pp. 14-15), a linear combination of asymptotic
>> expansions of two functions is an asymptotic expansion of the same
>> linear combination of the two functions. The same point appears in my
>> notes on Hinch (1991, _Perturbation methods_, Cambridge University
>> Press, Cambridge, p. 22). A limit has to be asymptotic to the thing
>> it's the limit of, no?
> no.
>
I think they say in the theorems on limits "if the limits exist", so it is not unconditionally true. So limit(a) may
not exist which sometimes means it is inf or minf or unsigned infinity or complex infinity or ind. Consider
limit(cos(x)^2 + sin(x^2), x ,inf);
>> How does all this sit together?
> read about limits, instead. I think you will find that
>
> lim(a+b) = lim(a)+lim(b) if lim(a) and lim(b) are finite, or at least one of them is finite.
>
> RJF
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