Consider the following function. F(x)=²²a=0₁ n=3, 05x50.1 (a) Approximate f by a Taylor polynomial with degreen at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) 7 (x) when x lies in the given interval. (Round your answer to five decimal places.) IR₂(x)| s

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 10E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...
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Consider the following function.
f(x)=²x², a = 0, n=3, 0 ≤x≤0.1
(a) Approximate f by a Taylor polynomial with degreen at the number a.
T₂(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T(x) when x lies in the given interval. (Round your answer to five decimal places.)
IR₂(x)| ≤[
Transcribed Image Text:Consider the following function. f(x)=²x², a = 0, n=3, 0 ≤x≤0.1 (a) Approximate f by a Taylor polynomial with degreen at the number a. T₂(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T(x) when x lies in the given interval. (Round your answer to five decimal places.) IR₂(x)| ≤[
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