Consider finding a rational function p(x) = (a + bx)/(1 + cx) that satisfies p(x,) = yi i = 1,2,3 %3D with x,, x2, x, distinct. Does such a function p(x) exist, or are additional conditions needed to ensure existence and uniqueness of p(x)? For a

Consider finding a rational function p(x) = (a + bx)/(1 + cx) that satisfies p(x,) = yi i = 1,2,3 %3D with x,, x2, x, distinct. Does such a function p(x) exist, or are additional conditions needed to ensure existence and uniqueness of p(x)? For a

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 11T: Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6...

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Question

12.
Consider finding a rational function p(x) = (a + bx)/(1 + cx) that
satisfies
p(x;) = y;
i = 1,2,3
with x,, x2, x, distinct. Does such a function p(x) exist, or are additional
conditions needed to ensure existence and uniqueness of p(x)? For a
general theory of rational interpolation, see Stoer and Bulirsch (1980,
р. 58).

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