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What are the practical applications of limits of function?
well derivatives cannt be used without limits so it is application for calculus
What is the History of differential calculus?
http://en.wikipedia.org/wiki/History_of_calculus Have a look at this wikipedia article. It has a great history of calculus.
Why is calculus described as understanding something by looking at small pieces?
Both derivatives and integrals - two of the most important concepts in calculus - are defined in terms of limits; specifically, what happens when something gets smaller and smaller.
What is mathematical analysis?
Analysis can be thought of as a continuation of calculus. It deals with topics such as measure, limits, and integration/differentiation, and spaces (such as metric spaces).
Mathematical field calculus?
Calculus is mainly about limits, which in turn are used to calculate the slope of a line (known as the "derivative"; lots of applications for that), and to calculate the area under a curve (the "integral" - also lots of applications for that). For more details, read the Wikipedia article on "Calculus", or read an introductory book on calculus. As prerequisites, you should be well-acquainted with high-school algebra.
