Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55

CAL2.113 Monotonicity and Boundedness of Sequences Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.113 Monotonicity and Boundedness of Sequences. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.113 Monotonicity and Boundedness of Sequences - Select whether a sequence is increasing, decreasing, bounded, and potentially convergent. Standards tags: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; 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 CAL2.113 Monotonicity and Boundedness of Sequences skill assessments:

Problem 1Difficulty: Mastery
For n >= 1, let a_n = (4n - 1)/(n + 2). Which proof gives the correct classification?
Aa_(n+1)-a_n = 9/((n+2)(n+3)) > 0 and a_n < 4, so the sequence is increasing, bounded above, and convergent
BThe denominator grows, so the sequence must decrease and converge to 0
CThe numerator grows, so the sequence is increasing and unbounded
DThe first two terms are enough to prove the sequence is bounded
Solution & Explanation:The difference calculation proves monotonicity for all n, and a_n < 4 gives an upper bound. Therefore the sequence is increasing, bounded, and convergent; checking only a few terms would not be enough.
Problem 2Difficulty: Mastery
A bounded sequence has b_(2k) -> 0 and b_(2k-1) -> 1. Which classification is correct?
AIt converges because it is bounded
BIt is bounded but not convergent
CIt must be increasing
DIt must be decreasing
Solution & Explanation:The even and odd subsequences approach different limits, so the full sequence cannot converge. Boundedness alone is not enough for convergence.
Problem 3Difficulty: Mastery
A sequence is decreasing and satisfies a_n >= 2 for every n. Which conclusion follows from the monotone convergence theorem?
AIt converges to some limit L with L >= 2
BIt must converge exactly to 2
CIt is unbounded below
DIt cannot converge because it is decreasing
Solution & Explanation:A decreasing sequence that is bounded below is convergent. The lower bound 2 guarantees the limit is at least 2, but the exact value need not be 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.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55 (Select whether a sequence is increasing, decreasing, bounded, and potentially convergent. Standards tags: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55).

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