Please explain each step!

PART I

1. Compute the Maclaurin polynomials of degree one, two, and three for f (x) = e-2x. 2. Compute the Taylor polynomial T2(x) for f(x) = arctan x about the point c = 1. 3. Compute the Maclaurin polynomial My(x) for f(x) = (1+ x) 3. 4.(a) Compute the Maclaurin polynomial M2(x) for f(x) = cos x. (b) Use the polynomial of part (a) to estimate cos 12 (c) Use a calculator to compute the error made using the estimate from part (b) for the value of cos 17 . Remember that the error is defined to be the absolute value of the difference between the true value and the estimate. 5. Let Mn(x) be the n Maclaurin polynomial for f(x) = et as given in the text. Use the error formula to determine a value of n so that | M,(2) - e?|