Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55

CAL2.147 Lagrange Error Bound Worksheet

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Q: What grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55 (Select the correct Lagrange remainder bound and use it to guarantee an accuracy. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55).

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.147 Lagrange Error Bound. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.147 Lagrange Error Bound - Select the correct Lagrange remainder bound and use it to guarantee an accuracy. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.147 Lagrange Error Bound skill assessments:

Problem 1Difficulty: Mastery

A planned table gives ∣f^(4)(t)∣ <= 4 on [0,0.1] and ∣f^(4)(t)∣ <= 7 on [0.1,0.3]. If P_3 centered at 0 is used to approximate f(0.25), which Lagrange bound is justified?

A4(0.25)⁴/4!

B7(0.25)⁴/4!

C7(0.25)³/3!

D4(0.3)⁴/4!

Solution & Explanation:The relevant interval is [0,0.25], which crosses both table intervals, so M must be at least the larger listed bound, 7. With degree 3, the Lagrange bound is 7(0.25)⁴/4!.

Problem 2Difficulty: Mastery

Two Taylor approximations are proposed for the same value. Approximation A has a Lagrange bound 0.003, and approximation B has a Lagrange bound 0.0007. Which conclusion is justified for a required tolerance of 0.001?

AOnly approximation A is guaranteed.

BOnly approximation B is guaranteed.

CBoth approximations are guaranteed.

DNeither approximation is guaranteed.

Solution & Explanation:A bound must be less than or equal to the tolerance to guarantee the accuracy. Approximation B has 0.0007 < 0.001, while approximation A has 0.003 > 0.001.

Problem 3Difficulty: Mastery

A calculator will display a value rounded to the nearest hundredth. Which Lagrange bound is sufficient to guarantee the displayed hundredth is correct?

AError < 0.01

BError < 0.005

CError < 0.05

DError < 0.1

Solution & Explanation:To guarantee rounding to the nearest hundredth, the error must be less than half of 0.01, which is 0.005. Confusing the place value with half the place value is a common accuracy mistake.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this CAL2.147 Lagrange Error Bound worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this CAL2.147 Lagrange Error Bound worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice CAL2.147 Lagrange Error Bound online with instant feedback?

Yes! In addition to this printable worksheet, students can practice CAL2.147 Lagrange Error Bound interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55 (Select the correct Lagrange remainder bound and use it to guarantee an accuracy. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55).