Lagrange Error Bound

AP Calculus · Axiom Academy

Quantifying how close a Taylor polynomial is to the true function If P_n(x) is the n th Taylor polynomial of f at a , then: Approximate e^ 0.1 using P_3(x) for e^x at a = 0 . Bound the error. P_3(0.1) = 1 + 0.1 + 0.005 + 0.000167 = 1.105167 The bound uses the (n+1) th derivative M is the maximum of |f^ (n+1) | on the interval This is heavily tested on the AP BC exam

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