Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about x = xo and then find the nth Taylor polynomial for the function in sigma notation. 5 In(x); 2o = e Po(x) =| p1(x) = P2(x) = P3(x) = p1(x) = k = +

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Find the Taylor polynomial T2(x) and compute the error |f(x) – T2(x)| for the given values of a and æ. f(x) = esin(z), a = x = 1.5 (Round your answer to six decimal places.) T2(1.5) = (Round your answer to two decimal places.) |f(1.5) – T2(1.5)| = X10 4

One of the two sets of functions, f1, f2, f3, or g1, 92, 93, is graphed in the figure to the left below; the other set is graphed in the right figure. Points A and B each have x = 0. Taylor polynomials of degree 2 approximating these functions near x = 0 are as follows: f1(x) - 5 +x + 2x? 91(x) - 2 - x + 2x2 f2(x) 2 5 + x – x2 92(x) z 2 + x + 2x? f3(x) 2 5 + x + x? 93(x) z 2 – x + x². II. B (a) Match the functions to the appropriate figure: f matches || g matches | v (b) What are the coordinates of the points A and B? A = В - (c) Match each function with the graphs (a)--(c) in the appropriate figure. fi = ? f2 ? f3 = ? 91 = ? 92 = ? 93 = ? > > > ||

Find the Taylor polynomial of degree 3, centered at a = 3 for the function f(x) = √√x + 4. Check Answer

Find the Taylor scries of f(x) = at a = 4. 2-8r+17

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A graphing calculator is recommended. Find the Taylor polynomial T,(x) for the function f centered at the number a. f(x) = In(x), a = 1 Graph fandT, on the same screen. y y y 2- 3- 1 2 -1 -1 2 3 -2 -4 -3 2 1 2