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Topic: should CAS resturn infinity for divergent integral or a message that
integral diverges?

Replies: 9   Last Post: Apr 19, 2014 1:49 AM

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Richard Fateman

Posts: 1,539
Registered: 12/7/04
Re: should CAS resturn infinity for divergent integral or a message
that integral diverges?

Posted: Mar 20, 2014 6:44 PM
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On 3/18/2014 1:35 PM, Axel Vogt wrote:
> PS: big grin for limit cos(x) or sin(x) = interval. I consider
> such as a smart answer by Maple, giving an interval as estimate,
> indicating "system gives up for details"

I suppose one can have a discussion on whether this is helpful
or meaningful, or consistent with the notion of interval.

I tend to think of an interval [-1,1] to mean that the true result
is a particular number v such that -1<=v<=1. In the limit
example, the result is apparently saying that there is no such v.
Rather the value as x->oo is bounded.

And then there are these problems.

we know that if lim f(x) = A and lim g(x) = B then lim f(x)*g(x) = AB

from these programs we learn that lim sin(x) = lim cos(x) = [-1,1]
also of course lim sin(2*x) = [-1,1].
putting these results together with

sin(2*x) = 2*sin(x)*cos(x)

and take the limit as x->oo we learn that
[-1,1] = 2*[-1,1]*[-1,1] = [-2,2].

Backtrack here and try to figure out what we did that went wrong.

<< exercise for the reader>>

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