Lagrange Error Bound Worksheet

This worksheet focuses on understanding and applying the Lagrange Error Bound to approximate functions using Taylor polynomials.

Grade 9 Math CalculusLagrange Error Bound

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.BF.B.3

Topics

CalculusLagrange Error BoundTaylor PolynomialsApproximation

7 sections · Free to use · Printable

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Lagrange Error Bound Worksheet

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Read each question carefully and show all your work. Use the Lagrange Error Bound to estimate the maximum error in the approximations.

1. State the formula for the Lagrange Error Bound (Remainder Estimation Theorem) for a Taylor polynomial of degree n centered at a.

2. The Lagrange Error Bound helps us find the possible error when approximating a function with a Taylor polynomial.

3. To use the Lagrange Error Bound, we need to find the maximum value of the (n+1)th of the function on the interval of interest.

4. If a Taylor polynomial of degree 2 is used to approximate a function f(x), what derivative is needed for the Lagrange Error Bound?

First derivative

Second derivative

Third derivative

Zeroth derivative

5. Consider the function f(x) = e^x. Approximate e^0.5 using a Taylor polynomial of degree 2 centered at x=0. Then, use the Lagrange Error Bound to find an upper bound for the error in your approximation.

6. The Lagrange Error Bound gives the exact error of the approximation.

True

False