Master Taylor & Power Series, Interval of Convergence Calc 2

Master Maclaurin, Taylor, and Power Series with clear step-by-step methods for Calculus 2 and AP Calculus BC exams

What you'll learn
- Determine the radius and interval of convergence for a given power series using ratio, root, and other convergence tests.
- Write power series representations for functions and manipulate them through differentiation and integration.
- Derive and apply Maclaurin and Taylor series expansions to approximate functions near a given point.
- Recognize and recall common series expansions (e.g., 𝑒 𝑥 e x , sin ⁡ 𝑥 sinx, cos ⁡ 𝑥 cosx, 1 1 − 𝑥 1−x 1 ​ ) for use in problem solving.
- Apply the Alternating Series Estimation Theorem to determine the accuracy of alternating series approximations.
- Use Taylor’s Remainder Theorem to bound the error of Maclaurin and Taylor polynomial approximations for non-alternating series.
- Apply series methods to solve exam-style Calculus 2 / AP BC problems with speed and accuracy.

Requirements
- A basic understanding of Calculus 1 topics (limits, derivatives, and basic integrals).
- en/pencil and paper for note-taking; a scientific calculator is optional.

Description
Master Taylor & Power Series, Interval of Convergence for Calculus 2 with Woody Calculus — the proven, step-by-step approach to conquering Infinite Series. In this course, you’ll build confidence through clear explanations, pattern recognition, and plenty of guided examples designed to make even the most challenging problems approachable.

You’ll start withPower Series fundamentals, learning exactly how to represent functions as series and determine their radius and interval of convergence. From there, you’ll move intoMaclaurin and Taylor Series, discovering how to create accurate polynomial approximations of functions and when to use them. You’ll also see how to applyTaylor’s Remainder Theoremto non-alternating series to bound approximation errors, and use theAlternating Series Estimation Theoremto achieve precise accuracy in alternating series problems.

Every lesson comes withdownloadable notes, fully worked examples, and problem-solving strategies designed to speed up recognition and execution — critical skills for exams. You’ll not only learn the methods, but also when and why to apply them, ensuring you can approach any Infinite Series question with confidence.

Whether you’re currently enrolled in Calculus 2, preparing for the AP Calculus BC exam, or brushing up on your skills for future courses, this class gives you the clarity, structure, and confidence to excel.

Join now and master the Infinite Series portion of Calculus 2 the Woody Calculus way — direct, structured, and built for results.

Who this course is for:
- Calculus 2 students who want a clear, step-by-step approach to mastering power series, Maclaurin series, Taylor polynomials, and intervals of convergence.
- AP Calculus BC students preparing for the Infinite Series portion of the exam.
- College students looking to strengthen their skills in series methods before exams or finals.
- Self-learners and math enthusiasts who want to understand Infinite Series from the ground up, with clear explanations and plenty of worked examples.
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