Let f be a function that has derivatives of all orders for all real numbers and let P2(x) be the second- degree Taylor polynomial for f about x = 0. The Taylor series for fabout x = 0 converges at x = x = ²1/1₁ and f(n) (x)| ≤ 1² for 2 ≤ n ≤ 5 and all values of x. n²+2 Find the smallest value of k for which the Lagrange error bound guarantees |f () - P₂ () ≤k.
Let f be a function that has derivatives of all orders for all real numbers and let P2(x) be the second- degree Taylor polynomial for f about x = 0. The Taylor series for fabout x = 0 converges at x = x = ²1/1₁ and f(n) (x)| ≤ 1² for 2 ≤ n ≤ 5 and all values of x. n²+2 Find the smallest value of k for which the Lagrange error bound guarantees |f () - P₂ () ≤k.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Let f be a function that has derivatives of all orders
for all real numbers and let P2₂(x) be the second-
degree Taylor polynomial for f about x = 0. The
Taylor series for fabout x = 0 converges at x
n²-1
and f(n) (x)| ≤ for 2 ≤ n ≤ 5 and all values of x.
n²+2
Find the smallest value of k for which the Lagrange
error bound guarantees f() - P₂ ) ≤k.
2
(4%
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