# 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 Lagrange error bound when using the second Taylor polynomial for the function at to approximate the value . Round to five decimal places.

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• B
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• D
• E

Q2:

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

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Q3:

Find the Lagrange 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 Lagrange 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.

• A15
• B17
• C16
• D19
• E18

Q9:

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

• A14
• B10
• C13
• D12
• E11

Q10:

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

Q11:

Find the error bound when using the fourth Taylor polynomial for the function at to approximate the value of . Give your answer in scientific form to three significant figures.

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Q12:

Find the error bound when using the second Taylor polynomial for the function at to approximate the value of . Give your answer in scientific form to three significant figures.

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• E

Q13:

Find the error bound when using the third Maclaurin polynomial for the function to approximate the value of . Give your answer to five decimal places.

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• E

Q14:

Find the error bound when using the third Taylor polynomial for the function at to approximate the value of .Give your answer in scientific form to three significant figures.

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Q15:

Find the error bound when using the third Maclaurin polynomial for the function to approximate the value of . Give your answer in scientific form to three significant figures.

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• B
• C
• D
• E