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  3. ZuAI AP College Board Calculus AB/BC
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Lagrange Error Bound

Next Topic - Radius and Interval of Convergence of Power Series
Study Guide Overview

This guide covers the Lagrange Error Bound for Taylor and Maclaurin Polynomials. It reviews constructing Taylor polynomials and explains how to use the Lagrange Error Bound to determine the maximum error of a Taylor polynomial approximation. The guide includes examples and a practice AP FRQ problem involving the Lagrange Error Bound.

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Previous Topic - Finding Taylor Polynomial Approximations of FunctionsNext Topic - Radius and Interval of Convergence of Power Series

Question 1 of 9

What is the general formula for a Taylor polynomial of a function f(x) centered at x=a?

f(x)=f(a)+f′(a)(x−a)+f′′(a)(x−a)2+...f(x)=f(a)+f'(a)(x-a)+f''(a)(x-a)^2+...f(x)=f(a)+f′(a)(x−a)+f′′(a)(x−a)2+...

f(x)=f(a)+f′(a)x+f′′(a)x22!+f′′′(a)x33!+...f(x)=f(a)+f'(a)x+\frac{f''(a)x^2}{2!}+\frac{f'''(a)x^3}{3!}+...f(x)=f(a)+f′(a)x+2!f′′(a)x2​+3!f′′′(a)x3​+...

f(x)=f(a)+f′(a)(x−a)+f′′(a)(x−a)22!+f′′′(a)(x−a)33!+...+f(n)(a)(x−a)nn!f(x)=f(a)+f'(a)(x-a)+\frac{f''(a)(x-a)^2}{2!}+\frac{f'''(a)(x-a)^3}{3!}+...+ \frac{f^{(n)}(a)(x-a)^n}{n!}f(x)=f(a)+f′(a)(x−a)+2!f′′(a)(x−a)2​+3!f′′′(a)(x−a)3​+...+n!f(n)(a)(x−a)n​

f(x)=f(a)+f′(a)(x−a)+f′′(a)(x−a)2+f′′′(a)(x−a)3+...f(x)=f(a)+f'(a)(x-a)+f''(a)(x-a)^2+f'''(a)(x-a)^3+...f(x)=f(a)+f′(a)(x−a)+f′′(a)(x−a)2+f′′′(a)(x−a)3+...