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This problem studies the rational function: r ( x ) = ( 4 x 4 5 9 x 3 + 3 2 4 x 2

This problem studies the rational function: r(x)=(4x459x3+324x2751x +622)/(x414x3+72x2151x +112)(a) Apply Horners rule twice (once for the numerator and once for the denominator)
to produce two plots, one for x =1.606+252i and one for x =2.400+252i. Your
results should look like Fig. 2.3.
(b) Create a new Python function that codes up the following expression:
s(x)=43(x 2)[(x 5)2+4]/(x +(x 2)2[(x 5)2+3]) which is a rewritten version of our rational function. Apply this new function to the
case of the previous two plots and compare the rounding error pattern, size, etc.
(c) Now introduce two more sets of results, this time for the starting expression for
r(x) produced using (not Horners rule but) the naive implementation, using powers
(i.e., the way you would have coded this up before doing the previous problem).
Interpret your findings in python

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