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Trouble with Limit[I ... k]/k, k-> Infinity]


I am struggling to valuate an intermediate result in a long calculation
and I get stuck with terms like this one:

Limit[Exp[I k A]/k, k -> Infinity, Assumptions -> {A != 0, A \[Element]
Reals}]

In the actual expression, A are somewhat more complicated expressions but
I am willing to tell Mathematica by hand that they are real and
non-zero, however, it still doesn't work. I don't see that there is a
problem in mathematical terms so how can I convince Mathematica to
give me an answer?

Actually, Mathematica 5.1 does not mind telling me the result of

Limit[Exp[I k]/k, k -> Infinity]

At the moment I am relying on a kludge relying on pattern-matching but I
am not very good at it so there might be a point to help me on.
Any input or help will be greatly appreciated.


Thanks,

Christian


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