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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
5-18 Mathematical Methods
choose two numbers a and b such that f ( a) and f ( b)
are of opposite signs so that the graph y = f ( x) crosses
the x-axis between x = a and x = b. This shows that a
root lies between a and b and we have f ( a) f ( b) < 0
(Figure 5.5(b)).
The equation of the chord joining the points
A = (a, f ( a)) and B = (b, f ( b)) is
() ()
() ( )
fb fa
yfb xa
ba
−=
(5.21)
The method consists of replacing the curve
y = f ( x) between
A and B by the chord AB and taking
the x-coordinate of the point of intersection of the
chord with the x-axis as an approximation to the root.
Thus a first approximation to the root is given by
1
()
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Publisher Resources

ISBN: 9781299446557Publisher Website