I don't really understand your question, since you say you are 'learning computer science theory and calculus comes up' it would appear that you have the answer

I don't really understand your question, since you say you are 'learning computer science theory and calculus comes up' it would appear that you have the answer to "What is calculus used for in Computer Science?" already. In the interest of trying to be helpful, I'll provide some of my some of my thoughts after completing a Computer Science degree at a large research university in the US. The vast majority of computer science THEORY involves discrete math, at least at the undergraduate level. There are numerous APPLICATIONS that use calculus and some of them have already been mentioned. Initially I thought it odd that we were required to complete multi-variable calculus for our degree, which seemed to have little to do with the 'discrete' math world and more with 'continuous' math topics. However as time went on I encountered topics in advanced courses where you were expected to be familiar calculus at that level. The notable exception to the lack of calculus in computer science 'theory' that I recall relates to Probability, as it is used in algorithm analysis. Hope I didn't misunderstand your question completely.