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Calculus I pp 67-71 | Cite as

Newton’s Method

  • Brian Knight
  • Roger Adams

Abstract

Many of the equations arising in practical problems are of a type difficult or impossible to solve by the standard algebraic methods. For example, the equations:
$$ 2\sin {\kern 1pt} x - x = 0{\kern 1pt} {\kern 1pt} {e^x} - 2x - 1 = 0,{\kern 1pt} {\kern 1pt} {x^6} - 3x + 1 = 0 $$
have roots which we may estimate, by graphing the functions and finding where the graphs cut the x-axis, but which we cannot find exactly. In these cases a numerical procedure known as Newton’s method allows us to use a value x 0 which is an approximate root of the equation:
$$ f(x) = 0 $$
in order to obtain a better approximation x 1.

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Copyright information

© Springer Science+Business Media New York 1975

Authors and Affiliations

  • Brian Knight
    • 1
  • Roger Adams
    • 2
  1. 1.Goldsmiths’ CollegeLondonUK
  2. 2.Thames PolytechnicLondonUK

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