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.

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