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Strictly speaking there is NO use of Calculus in computer science.  It is possible to use computer programming to approximately solve problems in Calculus but I would not call that "using Calculus in computer science.

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1 hour ago, Country Boy said:

It is possible to use computer programming to approximately solve problems in Calculus but I would not call that "using Calculus in computer science.

The question was not about using computers to solve calculus problems anyway. 

Since computer science is mainly about proving asymptotic behavior of the maximal running time of algorithms, there are lots of results in computer science that cannot or only with some extra difficulty be proved without calculus, e.g. typically using that the limit behavior is given by a suitable Riemann integral. Generally you cannot escape using limits to get general bounds on running time.

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