Taylor Series, Coefficients & Polynomials: Definition, Equations & Examples


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The Taylor series is most accurate:

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1. Let's say you want to write the Taylor series for f(x) = ex. The first term is _____.

2. You are asked to write the first two terms of the Taylor series for f(x) = sin x. Your result is _____.

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About This Quiz & Worksheet

In this informative quiz/worksheet combo, our instructors have designed short, multiple-choice questions to help you gauge your understanding of coefficients, polynomials and the Taylor series. These questions ask you about the point where the Taylor series is most accurate, how to identify the first and second terms in a series from an example problem and how to evaluate a Taylor series.

Quiz & Worksheet Goals

When you take this quiz, you'll be asked to:

  • Detail the point where the Taylor series is most accurate
  • Write the first term in a Taylor series in an example problem
  • Identify the first two terms of the Taylor series for an example equation
  • Evaluate a Taylor series when given example values
  • Discuss the relationship between x and a in order to get the best Taylor series approximation

Skills Practiced

  • Problem solving - use acquired knowledge to solve Taylor series practice problems
  • Knowledge application - use your knowledge to answer questions about where a Taylor series is the most accurate
  • Reading comprehension - ensure that you draw the most important information from the related math lesson
  • Interpreting information - verify that you can read information regarding the relationship between x and a in a Taylor series and interpret it correctly

Additional Learning

To help you learn more about this topic, we've created a lesson called Taylor Series, Coefficients & Polynomials: Definition, Equations & Examples. After you review this lesson, you should understand how to:

  • Explain what a Taylor series does to complicated functions
  • Define a Taylor polynomial
  • Detail how the integral of the Gaussian function is written