Taylor Polynomial T4(x) and Error Bound for f(x) = x^(1/12), a = 1, x = 1.4

Math Problem Statement

Find the Taylor polynomial T4(x) and use the Error Bound to find the maximum possible size of the error.

f(x)=x112,a=1,x=1.4

(Use symbolic notation and fractions where needed.)

(Round your answer to three decimal places.)

{:|f(1.4)-T4(1.4)|≤◻,]×10-2

We need to find

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Taylor Polynomials
Error Bound Estimation
Symbolic Computation

Taylor Polynomial Formula: Tn(x) = Σ (f^k(a) / k!) * (x - a)^k, k=0 to n
Error Bound Formula: |f(x) - Tn(x)| ≤ (M / (n+1)!) * |x-a|^(n+1)

Taylor's Theorem
Lagrange Error Bound

Grades 11-12 or early college level

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