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

CAL2.150 Representing Functions with Power Series Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.150 Representing Functions with Power Series. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.150 Representing Functions with Power Series - Choose the power series representation and interval where it equals the original function. 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 CAL2.150 Representing Functions with Power Series skill assessments:

Problem 1Difficulty: Mastery
Choose the power series in powers of \((x+2)\) for \(f(x)=\frac{(x+2)2}{1+(x+2)3}\), including the interval of equality.
A\(\sum_{n=0}\infty(x+2)3n+2\); interval \((-3,-1)\)
B\(\sum_{n=0}\infty(-1)n(x+2)3n\); interval \((-3,-1)\)
C\(\sum_{n=0}\infty(-1)n(x+2)3n+2\); interval \((-1,1)\)
D\(\sum_{n=0}\infty(-1)n(x+2)3n+2\); interval \((-3,-1)\)
Solution & Explanation:Expand \(1/(1+(x+2)3)=\sum[-(x+2)3]n\), then multiply by \((x+2)2\). The condition \(∣x+2∣ <1\) gives \((-3,-1)\).
Problem 2Difficulty: Mastery
Which series represents \(f(x)=\frac{x-1}{1-(x-1)2}\), including the interval where it equals \(f\)?
A\(\sum_{n=0}\infty(x-1)2n\); interval \((0,2)\)
B\(\sum_{n=0}\infty(-1)n(x-1)2n+1\); interval \((0,2)\)
C\(\sum_{n=0}\infty(x-1)2n+1\); interval \((0,2)\)
D\(\sum_{n=0}\infty(x-1)2n+1\); interval \((-1,1)\)
Solution & Explanation:Use \(1/(1-(x-1)2)=\sum(x-1)2n\), then multiply by \(x-1\). The condition \(∣x-1∣ <1\) gives \((0,2)\).
Problem 3Difficulty: Mastery
Select the power series in powers of \((x-2)\) for \(f(x)=\frac{1}{9-(x-2)2}\), and give its interval of equality.
A\(\sum_{n=0}\infty\frac{(x-2)2n}{9n}\); interval \((-1,5)\)
B\(\sum_{n=0}\infty\frac{(x-2)2n}{9n+1}\); interval \((-1,5)\)
C\(\sum_{n=0}\infty\frac{(-1)n(x-2)2n}{9n+1}\); interval \((-1,5)\)
D\(\sum_{n=0}\infty\frac{(x-2)2n}{9n+1}\); interval \((-3,3)\)
Solution & Explanation:Factor \(9-(x-2)2=9(1-(x-2)2/9)\). The condition \(∣x-2∣ <3\) gives \((-1,5)\); the interval must be centered at 2.

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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 (Choose the power series representation and interval where it equals the original function. 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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