Limits and Continuity
Here we begin the study of calculus, one of the most useful branches of mathematics. In this introductory chapter, we ask how the value f(x) of a function varies as we vary the input. This involves the concept of limit, on which all of calculus depends. Here, it arises when we discuss the following question: if f is a real function and x is approximately equal to a, then must f(x) be approximately equal to f(a) ? This is an important question with significant implications. For example if we enter 1.4142 (an approximation to 
) on a calculator, and press the ‘sin’ key, then we assume that the displayed result is an ...
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