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6 Nov 2019
Construct the Taylor polynomials Pn, i (delta x) centered at a = 1 for f(x) = lnx; take n = 1, 2, 3, and 4. Obtain estimates for In 1.02 and In 1.2 using the four different Taylor polynomials you found in part (a), and determine the error in each of these estimates. Is the error that Pn,1 makes for In 1.02 only about 1/10n + 1 times the size of the error the same polynomial makes for In 1.2? Explain. For each n = 1,2,3, and 4, sketch the graph of the function y = Rn,1(delta x) = ln(l + delta x) - Pn-1( delta x) on the interval -0.3 le delta x le 0.3. Does your graph demonstrate that Rn,1( delta x) = O(n + 1)? How, or why not? Show transcribed image text
Construct the Taylor polynomials Pn, i (delta x) centered at a = 1 for f(x) = lnx; take n = 1, 2, 3, and 4. Obtain estimates for In 1.02 and In 1.2 using the four different Taylor polynomials you found in part (a), and determine the error in each of these estimates. Is the error that Pn,1 makes for In 1.02 only about 1/10n + 1 times the size of the error the same polynomial makes for In 1.2? Explain. For each n = 1,2,3, and 4, sketch the graph of the function y = Rn,1(delta x) = ln(l + delta x) - Pn-1( delta x) on the interval -0.3 le delta x le 0.3. Does your graph demonstrate that Rn,1( delta x) = O(n + 1)? How, or why not?
Show transcribed image text Keith LeannonLv2
13 Mar 2019