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(Steps Shown) Interpolation of rational functions. Please refer to Problem 8 from Homework 4 to help you with this question. Find a rational function f(t)=(c_1+c_2

Question: Interpolation of rational functions. Please refer to Problem 8 from Homework 4 to help you with this question.

Find a rational function

\[f(t)=\frac{c_{1}+c_{2} t+c_{3} t^{2}}{1+d_{1} t+d_{1} t^{2}}\]

that satisfies the following interpolation conditions:

\[\begin{array}{llll} f(1)=2, & f(2)=5, & f(3)=9, & f(4)=-1, & f(5)=-4 \end{array}\]

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