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Differentiation

  • John Gilbert
  • Camilla Jordan
Part of the Palgrave Mathematical Guides book series (MG)

Abstract

In order to discuss continuity we need to consider ideas of limits. Consider the function f defined by
$$f(x) = \left\{ {\begin{array}{*{20}{c}} {2x + 1}&:&{x < 2} \\ {2x}&:&{x \geqslant 2} \end{array}} \right.$$
whose graph is shown in Figure 3.1. Let us see how we should show the function at x = 2. We cannot give it two values, since the value of f (2) is unique, and specified by the definition to be 4. In graphical terms, we could depict this by putting a small open circle at (2, 5) and a filled circle at (2, 4) as in Figure 3.1.

Keywords

Chain Rule Simple Pendulum Standard Family Graphical Term Constant Velocity Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© John Gilbert & Camilla Jordan 2002

Authors and Affiliations

  • John Gilbert
    • 1
  • Camilla Jordan
    • 2
  1. 1.Department of MathematicsUniversity of LancasterLancasterUK
  2. 2.Open UniversityUK

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