Convergent Series Teacher Resources
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Riemann Sums and the Fundemental Theorem of Calculus
Students explore the Fundamental Theorem of Calculus. In the Calculus lesson, students investigate indefinite and definite integrals and the relationship between the two, which leads to the discovery of the Fundamental Theorem of Calculus.
AP Calculus Practice Exam: BC Version - Part A
In this calculus worksheet, students solve 28 multiple choice problems. Students find derivatives, volumes, limits, convergent series, etc.
Calculus Practice BC
In this calculus worksheet, students solve functions using the derivatives. They calculate the volume where the graph is revolving around the x-axis, a line, the y-axis and where x=e. There are 28 questions.
AP Calculus Practice Exam
In this calculus activity, students solve functions by taking the derivative of the equations. There are 28 questions using logs and trig functions.
Help your pupils define a Taylor polynomial approximation to a function f of degree n about a point x = a. After completing several problems with guided practice, individuals graph convergence of Taylor polynomials and use them to approximate function values.
Infinite Sequences and Series
Students investigate sequences and series numerically, graphically, and symbolically. In this sequences and series lesson, students use their Ti-89 to determine if a series is convergent. Students find the terms in a sequence and series and graph them. Students use summation notation to determine the sum of a sequence.
Sequences and Series on a Calculator
Students find patterns in a sequence. In this sequences and series lesson, students use their calculator to find the sequence of partial sums. They graph functions and explore convergent series. Students approximate alternating series.
Twenty-Eight Multiple Choice No Calculator Allowed AP Calculus BC Practice Exam
In this AP Calculus BC practice exam, students solve twenty-eight multiple choice problems without the use of a calculator. This worksheet should be completed in fifty-five minutes.
AP Calculus Practice Exam
In this Calculus worksheet, students are provided with problems of a similar nature to those on their exam. Problems include limits, derivatives, and integrals. The four page worksheet contains twenty-eight problems. Answers are not included.
Approximating Integrals with Riemann Sums
Learners practice calculating and analyzing Riemann sums and illustrate when Riemann sums will over/under-approximate a definite integral. They view how the convergence of Riemann sums as the number of subintervals get larger.
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.
Review of Calculus BC II
In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series. The one page interactive worksheet contains fifty-two problems. Answers are not provided.
Limit Examples w/ brain malfunction on first prob (part 4)
Sal explores more complex limit problems including showing how to take the limit of an expression with a square root by using the conjugate and how to simplify trigonometric functions that are part of limit problems. Note: A mistake is made on the last step of first problem where multiplication should have been used instead of addition, resulting in the correct answer of 3/16.
Infinite Geometric Series - ID: 9894
Students investigate geometric series. In this Algebra II/Pre-Calculus lesson, students use a spreadsheet application to create partial sums of geometric series and observe convergence and divergence. Students investigate the relationship between the behavior of the graph and the common ratio of the series. Students examine the formula for the sum of a divergent infinite geometric series.
Biological Models with Differential Equations
Explore differential equations by using models representing growth and decline. Using calculus, learners will investigate exponential and logistic growth in the context of several models representing the growth or decline of a population. Most of the models have a closed-form solutions. Problems and solutions are included.
Converge or Diverge?
Young scholars prepare for the calculus concepts of limits by examining sequences that converge and diverge. By using an Excel program that generates sequences, students manipulate the starting number, multiplier and add-on values, and examine both the numerical and graphical representations of the sequence.
Identify the limits. Using geometry, learners will define the limit and fundamental theorem of calculus. They will also relate limit and derivatives to the real world.
In 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.
Students solve problems using implicit differentiation. In this calculus lesson, students take the derivative to calculate the rate of change. They observe two robots and draw conclusion from the data collected on the two robots.
In this college level Calculus worksheet, students examine sequences to determine if they are increasing, decreasing, or non monotonic. Students find the sum of series and determine if they diverge. The one page worksheet contains twenty-one problems. Answers are not provided.