Let f(x) = ln(3-x). (a) Find the 2nd order Taylor polynomial for f(x) centered at x = 2. (b) Use T/(x; 2) to approximate In (0.9). Round to 4 decimal places. (c) If |x-2] ≤ 0.1, find a "reasonable" upper bound on error when using T²(x; 2) to estimate f(x). Round to 4 decimal places past the leading 0s.
Let f(x) = ln(3-x). (a) Find the 2nd order Taylor polynomial for f(x) centered at x = 2. (b) Use T/(x; 2) to approximate In (0.9). Round to 4 decimal places. (c) If |x-2] ≤ 0.1, find a "reasonable" upper bound on error when using T²(x; 2) to estimate f(x). Round to 4 decimal places past the leading 0s.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f(x) = ln(3-x). (a) Find the 2nd order Taylor polynomial for f(x) centered at x = 2. (b) Use T/(x; 2) to approximate In (0.9). Round to 4 decimal places. (c) If |x-2] ≤ 0.1, find a "reasonable" upper bound on error when using T²(x; 2) to estimate f(x). Round to 4 decimal places past the leading 0s.
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