contradictory results with limit

[lukamar]

Hello,
the command

Code : Tout sélectionner

limit(acos(1-x^2)/ln(1+x),x,0)

gives sqrt(2), but this limit does not exists actually. If one inputs

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limit(acos(1-x^2)/ln(1+x),x,0,-1); limit(acos(1-x^2)/ln(1+x),x,0,1)

the correct results -sqrt(2) and sqrt(2), respectively, are obtained. One-sided limits differ (because ln(1+x) changes sign), so limit can't exist.

By the way, what's the purpose of bounded_function? Function limit returns those in cases when limit does not exist and is not +/-infinity (for example, limit(sin(x),x,inf)). But wouldn't it be more convenient to just return undef in such cases?

[parisse]

That's because acos does not behave like an analytic function at 1, I will add a check in limit.
I keep bounded function because it is more informative than undef.