Continuous Functions

Read this section for an introduction to what we mean when we say a function is continuous. Work through practice problems 1 and 2.


We saw a few "nice" functions whose limits as \mathrm{x} \rightarrow \mathrm{a} simply involved substituting \mathrm{a} into the function: \lim\limits_{x \rightarrow a} \mathrm{f}(\mathrm{x})=\mathrm{f}(\mathrm{a}). Functions whose limits have this substitution property are called continuous functions, and they have a number of other useful properties and are very common in applications. We will examine what it means graphically for a function to be continuous or not continuous. Some properties of continuous functions will be given, and we will look at a few applications of these properties including a way to solve horrible equations such as \sin (x)=\frac{2 x+1}{x-2}.

Source: Dave Hoffman,
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