# Lesson Worksheet: Lagrange Error Bound Mathematics • Higher Education

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.

• A
• B
• C
• D
• E

Q2:

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

• A
• B
• C
• D
• E

Q3:

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 .

• A
• B
• C
• D
• E

Q4:

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

• A
• B
• C
• D
• E

Q5:

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

• A
• B
• C
• D
• E

Q6:

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

• A
• B
• C
• D
• E

Q7:

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

Q8:

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

Q9:

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

Q10:

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

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