Answer parts a through d using the function $f(x)=ln(1x)[8$ pts$]$

a$.$ Find the eighth degree Taylor polynomial, centered at $0,$ to approximate $f(x)=ln(1x).$ Be sure to simplify your answer.

b$.$ Using your eighth degree polynomial from part a and Taylor's Inequality, If $|f^{(n1)}(x)|M$ for $|x-a|d,$ then $|E_n(x)|=|f(x)-P_n(x)|\frac{M}{(n1)!}|x-a{|}^{(n1)}$ to find the magnitude of the maximum possible error in approximating $f(0\mathrm{.}1).$

c$.$ Approximate $ln(1\mathrm{.}1)$ using your eighth degree Taylor polynomial. What is the actual error? Is it smaller than your estimated error? Round your answer to enough decimal places so you can determine.

d$.$ Create and submit a plot of the function along with your Taylor Polynomial. Based on your plot, what appears to be the interval of convergence? Explain.