# Worksheet: Lagrange Error Bound

In this worksheet, we will practice using the Lagrange error bound (Taylor's theorem with remainder) to find the maximum error when using Taylor polynomial approximations.

**Q1: **

Find the error bound when using the second Taylor polynomial for the function at to approximate the value . Approximate to five decimal places.

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**Q2: **

Determine the least degree of the Maclaurin polynomials needed for , approximating where .

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**Q3: **

Find the error bound when using the third Maclaurin polynomial for the function at to approximate the value .

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**Q4: **

Determine the least degree of the Maclaurin polynomials needed to approximate the value of with an error less than 0.001 using the Maclaurin series of .

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**Q5: **

Find the error bound when using the third Talyor polynomial for the function at to approximate the value of .

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**Q6: **

Determine the least degree of the Maclaurin polynomials for , approximating where .

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**Q7: **

Determine the lowest degree of the Maclaurin polynomial needed to approximate the function in the interval with an error less than 0.001 .

**Q8: **

Determine the lowest degree of the Maclaurin polynomial needed to approximate the function in the interval with an error less than 0.001.

- A 17
- B 19
- C 18
- D 15
- E 16

**Q9: **

Determine the lowest degree of the Maclaurin polynomial needed to approximate the function in the interval with an error less than 0.001.

- A 14
- B 11
- C 12
- D 10
- E 13

**Q10: **

Determine the lowest degree of the Maclaurin polynomial needed to approximate the function on the interval with an error less than 0.001 .