calculus 2 series and sequences practice test

If it con-verges, nd the limit. /Filter /FlateDecode /Subtype/Type1 We will also give the Divergence Test for series in this section. 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 /Type/Font 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 Course summary; . If you'd like a pdf document containing the solutions the download tab above contains links to pdf's containing the solutions for the full book, chapter and section. Which of the following sequences follows this formula? << %PDF-1.5 (answer), Ex 11.4.6 Approximate \(\sum_{n=1}^\infty (-1)^{n-1}{1\over n^4}\) to two decimal places. ,vEmO8/OuNVRaLPqB.*l. Ex 11.11.5 Show that \(e^x\) is equal to its Taylor series for all \(x\) by showing that the limit of the error term is zero as \(N\) approaches infinity. In exercises 3 and 4, do not attempt to determine whether the endpoints are in the interval of convergence. Part II. (answer), Ex 11.9.3 Find a power series representation for \( 2/(1-x)^3\). )Ltgx?^eaT'&+n+hN4*D^UR!8UY@>LqS%@Cp/-12##DR}miBw6"ja+WjU${IH$5j!j-I1 This page titled 11.E: Sequences and Series (Exercises) is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by David Guichard. 777.8 777.8] We will also illustrate how the Ratio Test and Root Test can be used to determine the radius and interval of convergence for a power series. Solving My Calc 2 Exam#3 (Sequence, Infinite Series & Power Series) Good luck! Parametric equations, polar coordinates, and vector-valued functions Calculator-active practice: Parametric equations, polar coordinates, . (answer), Ex 11.10.9 Use a combination of Maclaurin series and algebraic manipulation to find a series centered at zero for \( x\cos (x^2)\). /Name/F5 Ex 11.1.1 Compute \(\lim_{x\to\infty} x^{1/x}\). Each review chapter is packed with equations, formulas, and examples with solutions, so you can study smarter and score a 5! Applications of Series In this section we will take a quick look at a couple of applications of series. The Root Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. A proof of the Root Test is also given. << We will illustrate how partial sums are used to determine if an infinite series converges or diverges. 833.3 833.3 833.3 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 Which of the following sequences is NOT a geometric sequence? Math 129 - Calculus II. Khan Academy is a 501(c)(3) nonprofit organization. |: The Ratio Test shows us that regardless of the choice of x, the series converges. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. (answer). /Length 465 endstream endobj startxref /Type/Font 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. /Name/F1 Ex 11.9.5 Find a power series representation for \(\int\ln(1-x)\,dx\). stream 24 0 obj All rights reserved. /BaseFont/PSJLQR+CMEX10 Infinite series are sums of an infinite number of terms. MATH 126 Medians and Such. endobj 489.6 489.6 272 272 761.6 489.6 761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.9 Some infinite series converge to a finite value. /LastChar 127 (answer). Let the factor without dx equal u and the factor with dx equal dv. 5.3 The Divergence and Integral Tests - Calculus Volume 2 - OpenStax >> /FontDescriptor 8 0 R Choose the equation below that represents the rule for the nth term of the following geometric sequence: 128, 64, 32, 16, 8, . Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. More on Sequences In this section we will continue examining sequences. Which of the sequences below has the recursive rule where each number is the previous number times 2? 531.3 590.3 472.2 590.3 472.2 324.7 531.3 590.3 295.1 324.7 560.8 295.1 885.4 590.3 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 /FirstChar 0 /Widths[606.7 816 748.3 679.6 728.7 811.3 765.8 571.2 652.8 598 757.6 622.8 552.8 1 2 + 1 4 + 1 8 + = n=1 1 2n = 1 We will need to be careful, but it turns out that we can . At this time, I do not offer pdf's for solutions to individual problems. endobj >> Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. (answer). Alternating Series Test In this section we will discuss using the Alternating Series Test to determine if an infinite series converges or diverges. 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1) \(\displaystyle \sum^_{n=1}a_n\) where \(a_n=\dfrac{2}{n . Question 5 5. If you're seeing this message, it means we're having trouble loading external resources on our website. Indiana Core Assessments Mathematics: Test Prep & Study Guide. 8 0 obj May 3rd, 2018 - Sequences and Series Practice Test Determine if the sequence is arithmetic Find the term named in the problem 27 4 8 16 Sequences and Series Practice for Test Mr C Miller April 30th, 2018 - Determine if the sequence is arithmetic or geometric the problem 3 Sequences and Series Practice for Test Series Algebra II Math Khan Academy }\) (answer), Ex 11.8.3 \(\sum_{n=1}^\infty {n!\over n^n}x^n\) (answer), Ex 11.8.4 \(\sum_{n=1}^\infty {n!\over n^n}(x-2)^n\) (answer), Ex 11.8.5 \(\sum_{n=1}^\infty {(n! UcTIjeB#vog-TM'FaTzG(:k-BNQmbj}'?^h<=XgS/]o4Ilv%Jm 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 >> Sequences In this section we define just what we mean by sequence in a math class and give the basic notation we will use with them. /Widths[663.6 885.4 826.4 736.8 708.3 795.8 767.4 826.4 767.4 826.4 767.4 619.8 590.3 Then click 'Next Question' to answer the next question. Which of the following is the 14th term of the sequence below? Calculus II For Dummies Cheat Sheet - dummies Ex 11.1.3 Determine whether {n + 47 n} . 666.7 1000 1000 1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 endobj endstream stream 70 terms. Complementary General calculus exercises can be found for other Textmaps and can be accessed here. If you . stream 441.3 461.2 353.6 557.3 473.4 699.9 556.4 477.4 454.9 312.5 377.9 623.4 489.6 272] 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 Calculus II-Sequences and Series. Sequences and Series for Calculus Chapter Exam - Study.com AP Calculus AB and BC: Chapter 9 -Infinite Sequences and Series : 9.4 >> We will determine if a sequence in an increasing sequence or a decreasing sequence and hence if it is a monotonic sequence. Donate or volunteer today! 15 0 obj 5.3.2 Use the integral test to determine the convergence of a series. /Subtype/Type1 Which of the following is the 14th term of the sequence below? )^2\over n^n}(x-2)^n\) (answer), Ex 11.8.6 \(\sum_{n=1}^\infty {(x+5)^n\over n(n+1)}\) (answer), Ex 11.9.1 Find a series representation for \(\ln 2\). Each term is the product of the two previous terms. 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 Calculus (single and multi-variable) Ordinary Differential equations (upto 2nd order linear with Laplace transforms, including Dirac Delta functions and Fourier Series. Maclaurin series of e, sin(x), and cos(x). Series | Calculus 2 | Math | Khan Academy (answer), Ex 11.2.6 Compute \(\sum_{n=0}^\infty {4^{n+1}\over 5^n}\). Which equation below represents a geometric sequence? 9.8 Power Series Chapter 9 Sequences and Series Calculus II raVQ1CKD3` rO:H\hL[+?zWl'oDpP% bhR5f7RN `1= SJt{p9kp5,W+Y.e7) Zy\BP>+``;qI^%$x=%f0+!.=Q7HgbjfCVws,NL)%"pcS^ {tY}vf~T{oFe{nB\bItw$nku#pehXWn8;ZW]/v_nF787nl{ y/@U581$&DN>+gt Convergence/Divergence of Series In this section we will discuss in greater detail the convergence and divergence of infinite series. Estimating the Value of a Series In this section we will discuss how the Integral Test, Comparison Test, Alternating Series Test and the Ratio Test can, on occasion, be used to estimating the value of an infinite series.

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