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

CAL2.145 Taylor Polynomial Coefficients Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.145 Taylor Polynomial Coefficients. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.145 Taylor Polynomial Coefficients - Select the correct coefficients using derivatives at the center. 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

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Below are sample questions representative of the exercises included on this worksheet and related CAL2.145 Taylor Polynomial Coefficients skill assessments:

Problem 1Difficulty: Mastery
Suppose f^(n)(2) = (n + 1)! for every n >= 0. What is the coefficient of (x - 2)7 in the Taylor polynomial centered at x = 2?
A7
B56
C40320
D8
Solution & Explanation:The coefficient of (x-2)7 is f^(7)(2)/7!. Since f^(7)(2)=8!, the coefficient is 8!/7! = 8.
Problem 2Difficulty: Mastery
For f(x) = ex/(1 - x), what is the coefficient of x4 in the Maclaurin polynomial?
A8/3
B24/65
C65/24
D5/2
Solution & Explanation:The x4 coefficient in ex(1+x+x2+x3+x4+...) is 1 + 1 + 1/2 + 1/6 + 1/24 = 65/24.
Problem 3Difficulty: Mastery
For f(x) = x2 ln(1 + x), what is the coefficient of x5 in the Maclaurin polynomial?
A-1/3
B1/3
C1/5
D-1/4
Solution & Explanation:Since ln(1+x)=x-x2/2+x3/3-x4/4+... , multiplying by x2 makes the x5 coefficient equal to the x3 coefficient of ln(1+x), which is 1/3.

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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 coefficients using derivatives at the center. 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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