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Strangely enough, limit even gets this wrong if you feed it the

factored form:

limit ( (cos(1/x)-1) * sin(x), x, inf)

even though it correctly gets

limit(cos(1/x)-1,x,inf) => 0

and

limit(sin(x),x,inf) => ind

and 0*ind is always 0.

On the other hand, it does get it right if you factor the

exponentialized form:

limit(factor(ev(...,exponentialize)),x,inf) => 0