(j) Using Maple?s Taylor Approximation command, plot f(x) = x^2 e^ sin (X) toget

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(j) Using Maple?s Taylor Approximation command, plot f(x) = x^2 e^ sin (X) together with its first 8 Taylor Polynomials. On the printout, label f(x), and each of the Taylor Polynomials T1 (x) . . . T8(x). By studying the plot in part (j), estimate the domain over which TS(z) provides a good approximation for f(x) = X^2 e^sin (x) ESTIMATE: As n gets larger, what general statement can you make about using Tn(x) to approximate f(x) near some point X = a? Exercise 2 Find the maximum possible error in using the 4th degree Taylor Polynomial about x = 0 to approximate the function f(x) = in the interval No hints arc provided. Use the methods you tried in this lab and Exercise 1 to find the answer to this exercise. Remember to restart : Maple each time you start a new exercise. QUESTION: Does T4 (x) overestimate or underestimate f(x) in the interval Explain by referring to a plot of the difference between T4(x) and f(x). Indicate your answer on the print out of this plot. QUESTION: What is the maximum value of f(x) in the interval QUESTION: What is the maximum error in using T4(x) to approximate f(t) in the interval

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