Functions and Continuity
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Formal definition of a limit
Equations are omitted for technical reasons - download the original pdf
A function [Equation goes here - download the original pdf to see it.] tends to the limit l as x becomes larger and larger ('tends to infinity') if, when e is a given positive number, however small, a number N can be found, depending on e such that [Equation goes here - download the original pdf to see it.] This is abbreviated to [Equation goes here - download the original pdf to see it.] In this context we are discussing continuity, and the idea that a function defined piecewise may not converge uniquely on a single value, so that if we were drawing the graph of that function we would have to lift the pencil at that point. To capture this idea we modify the above definition as follows.
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Contents of
Functions and Continuity
1 Functions
2 Graph
3 Inverse of a Function: monotone increasing or decreasing functions
4 The reciprocal function - singularities
5 Functions defined piecewise on their domain
6 Limits
7 Formal definition of a limit
8 Formal definition of the limit of a function at a point x = a
9 Informal arguments
10 Continuity
11 Combining limits
12 Quotients
13 Image set
14 Inverse image
15 Odd and even functions
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