Texas Instruments
Convergence of Taylor Series
Students analyze taylor series for convergence. In this calculus instructional activity, students analyze the graph of a taylor series as it relates to functions. They use the TI calculator to graph and observe the different series.
College Board
AP® Calculus: Special Focus - Infinite Series
Read a series to develop an understanding of series. The special focus professional development on infinite series consists of eight articles. Articles contain information strictly for teachers along with aspects to incorporate into the...
Curated OER
Taylor Series
In this calculus worksheet, students solve various functions for the Taylor Series using a variety of solving methods including the double angle formula, partial fractions, and u substitution. There are 8 questions.
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Introduction to Taylor Series
In this Taylor Series activity, students explore functions with an infinite series. They complete an integral of convergence and explore the degree of the polynomials. This four-page activity contains four multi-step problems.
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Rates of Convergence of Functions and Sequences
In this math worksheet, learners explore the rates of convergence for functions and sequences. They also practice using Taylor series approximations.
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Intervals of Convergence
In this math worksheet, students examine the concept of intervals and how they converge. Then students apply the Taylor series for the problems.
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Taylor and Maclaurin Series
In this Taylor and Maclaurin series activity, learners answer 10 questions about Taylor and Maclaurin series. Students find the Taylor and Maclaurin series for trigonometric, exponential, and inverse functions at a given value.
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Taylor Series
In this Calculus worksheet, students use Taylor's inequality to show that the series converges to sin(x). The two page worksheet contains seven questions. Answers are not included.
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Taylor Seies
For this calculus worksheet, students find the Taylor series for each function adn give the interval where the series converges. The two page worksheet contains nine questions. Answers are not included.
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Worksheet 39 - Polar Coordinates
In this polar coordinates worksheet, students graph polar coordinates and determine the values of a given series. This one-page worksheet contains 14 multi-step problems.
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Worksheet 22
In this math activity, students determine using geometry the radius of convergence of the Taylor series centered at x0 = 0 for the function
College Board
2009 AP® Calculus BC Free-Response Questions Form B
Let them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...
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NUMB3RS - Season 2 - "Convergence" - Air Hockey
Learn how to use a matrix to organize data to solve a problem. This activity uses wins and losses to rank players for an air hockey tournament they wish to have. After practicing some basic matrix operations the class could do the...
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Error and Power Series
For this college level calculus worksheet, students compare two series to compute the error given the number of terms added. Students write the Maclaurin and Taylor series for the given functions. The two page worksheet contains seven...
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Worksheet 17
In this math learning exercise, learners practice graphing functions and define the domain. Then they use Lagrange's Theorem to estimate the error involved in using the two Taylor polynomials.
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Worksheet 21
In this math worksheet, students find the interval convergence of the series. They also practice writing a series and the functions. Students find the Taylor series about zero.
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Worksheet 12 - Spring 1996
In this math learning exercise, learners consider a series and test to see if the law of convergence applies or not. Then they calculate the Taylor series about x = 0 for the trigonometric functions f(x)=sinx and g(x)=cos.
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Worksheet 16 Practice Exam 1
In this math instructional activity, students consider the Taylor series and the Fibonacci sequence. They define the interval of convergence of the Taylor series.
Curated OER
Numeral Analysis: Rate of Convergence
In this rate of convergence worksheet, students use three different methods to compute an order of convergence of a function. This four-page worksheet contains approximately 10 problems, with examples.
College Board
2016 AP® Calculus BC Free-Response Questions
The split is 50-50. Released free-response questions from the 2016 AP Calculus BC show that half the questions are from the AB portion of the course and the others are from the BC portion. Teachers and pupils use the items to prepare and...
College Board
2014 AP® Calculus BC Free-Response Questions
How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...
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Worksheet 15
In this math worksheet, students sketch and label on a number line the regions that converge and diverge with the sequences. Then they examine a smooth function and define its series.
College Board
2012 AP® Calculus BC Free-Response Questions
Get better prepared. Individuals use the six released AP® Calculus BC free-response questions to practice for the actual exam. The questions contain two calculator items and four non-calculator items. Topics include particle movement,...
College Board
2005 AP® Calculus BC Free-Response Questions Form B
Let's put it in context. Pupils use the AP® Calculus BC free-response questions to practice for the exam. Five of the six released items deal with mathematical problems, with one using a real-world situation. Learners use differentiation...