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Lagrange Error Bound and Accuracy (BC Calculus - Unit 10)

Jean Adams
Grade Levels
11th - 12th, Higher Education
Formats Included
  • Zip
9 + 21 slides
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Lagrange Error Bound and Accuracy Lesson:
Your AP Calculus BC students will use Taylor polynomials to estimate values of functions, measure the accuracy and error bound.

What is included in this resource?

⭐ Guided Student Notes

Fully-editable SMART Board® Slides

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Full solution set

Lesson Objective:

★ Use Taylor polynomials to estimate values of functions

★ Use Taylor’s Inequality to measure the accuracy of approximations.

★ Use alternating series error bound to bound the error of a Taylor approximation of a function.


NOTE: This lesson has been updated to reflect the changes in the AP Calculus CED Binder .


College Board® Topics:

Topic 10.10: Alternating Series Error Bound

Topic 10.12: Lagrange Error Bound

College Board® Learning Objectives:

LIM-7.B: Approximate the sum of a series. (BC Only)
LIM-7.B.1: If an alternating series converges by the alternating series test, then the alternating series error bound can be used to bound how far a partial sum is from the value of the infinite series. (BC Only)

LIM-8.C: Determine the error bound associated with a Taylor polynomial approximation. (BC Only)

LIM-8.C.1: The Lagrange error bound can be used to determine a maximum interval for the error of a Taylor polynomial approximation to a function. (BC Only)

LIM-8.C.2: In some situations, the alternating series error bound can be used to bound the error of a Taylor polynomial approximation to the value of a function. (BC Only)

The unit includes the following topics:

1. Series and Convergence

2. The Integral Test and p-Series

3. Comparison of Series

4. Alternating Series

5. Ratio and Root Tests

6. Taylor Polynomials and Approximations

7. Lagrange Error Bound and Accuracy

8. Power Series and Interval of Convergence

9. Taylor and Maclaurin Series

10. Representing Functions by Power Series

Click HERE to SAVE 20% by buying all INFINITE SEQUENCES & SERIES products, including cooperative activities, in the UNIT 10 MEGA BUNDLE.

You may also be interested in:

Sequences & Series Essentials

Sequences & Series Assessments

Sequences & Series Homework

AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.



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Total Pages
9 + 21 slides
Answer Key
Teaching Duration
Lifelong tool
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