User:EGM6341.s11.TEAM1.Sujin.HW3

Find
Prove that Eq5.1 is equal to $$\begin{align}e^{(n+1)}(x)=f^{(n+1)}(x)- \cancelto{0}{f_n^{L(n+1)}(x)} \end{align}$$ using Eq5.2 thru Eq 5.4.

Solution
Suppose that $$ f(x) $$ is at leat $$ n+1 $$ times differentiable function. From Eqn.5.3, we can confirm that;

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Find
Prove Eq 6.1

Solution
Thus,

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