/Type/Font Boundary Value Problems & Fourier Series, 8.3 Periodic Functions & Orthogonal Functions, 9.6 Heat Equation with Non-Zero Temperature Boundaries, 1.14 Absolute Value Equations and Inequalities. >> (answer), Ex 11.11.3 Find the first three nonzero terms in the Taylor series for \(\tan x\) on \([-\pi/4,\pi/4]\), and compute the guaranteed error term as given by Taylor's theorem. /LastChar 127 Sequences In this section we define just what we mean by sequence in a math class and give the basic notation we will use with them. May 3rd, 2018 - Sequences and Series Practice Test Determine if the sequence is arithmetic Find the term named in the problem 27 4 8 16 Sequences and Series Practice for Test Mr C Miller April 30th, 2018 - Determine if the sequence is arithmetic or geometric the problem 3 Sequences and Series Practice for Test Series Algebra II Math Khan Academy Other sets by this creator. Determine whether the series is convergent or divergent. endobj 45 0 obj /Length 465 /Name/F1 Alternating Series Test - In this section we will discuss using the Alternating Series Test to determine if an infinite series converges or diverges. /Length 200 Each term is the difference of the previous two terms. Don't all infinite series grow to infinity? /BaseFont/PSJLQR+CMEX10 The numbers used come from a sequence. Choose your answer to the question and click 'Continue' to see how you did. Learn how this is possible, how we can tell whether a series converges, and how we can explore convergence in . Alternating series test. /Length 569 % 18 0 obj Worked example: sequence convergence/divergence, Partial sums: formula for nth term from partial sum, Partial sums: term value from partial sum, Worked example: convergent geometric series, Worked example: divergent geometric series, Infinite geometric series word problem: bouncing ball, Infinite geometric series word problem: repeating decimal, Proof of infinite geometric series formula, Level up on the above skills and collect up to 320 Mastery points, Determine absolute or conditional convergence, Level up on the above skills and collect up to 640 Mastery points, Worked example: alternating series remainder, Taylor & Maclaurin polynomials intro (part 1), Taylor & Maclaurin polynomials intro (part 2), Worked example: coefficient in Maclaurin polynomial, Worked example: coefficient in Taylor polynomial, Visualizing Taylor polynomial approximations, Worked example: estimating sin(0.4) using Lagrange error bound, Worked example: estimating e using Lagrange error bound, Worked example: cosine function from power series, Worked example: recognizing function from Taylor series, Maclaurin series of sin(x), cos(x), and e, Finding function from power series by integrating, Interval of convergence for derivative and integral, Integrals & derivatives of functions with known power series, Formal definition for limit of a sequence, Proving a sequence converges using the formal definition, Infinite geometric series formula intuition, Proof of infinite geometric series as a limit. Which rule represents the nth term in the sequence 9, 16, 23, 30? YesNo 2.(b). Math 1242: Calculus II - University of North Carolina at Charlotte Which of the following sequences is NOT a geometric sequence? At this time, I do not offer pdf's for . Consider the series n a n. Divergence Test: If lim n a n 0, then n a n diverges. The book contains eight practice tests five practice tests for Calculus AB and three practice tests for Calculus BC. 531.3 590.3 472.2 590.3 472.2 324.7 531.3 590.3 295.1 324.7 560.8 295.1 885.4 590.3 /BaseFont/UNJAYZ+CMR12 Here is a list of all the sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section. We will also determine a sequence is bounded below, bounded above and/or bounded. Power Series In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series. 816 816 272 299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 /Filter /FlateDecode /Filter[/FlateDecode] /FirstChar 0 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 6.5E: Exercises for Comparison Test - Mathematics LibreTexts This will work for a much wider variety of function than the method discussed in the previous section at the expense of some often unpleasant work.
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