When you have completed the free practice test, click 'View Results' to see your results. AP is a registered trademark of the College Board, which has not reviewed this resource. Math 129 - Calculus II. 0 A review of all series tests. << (answer), Ex 11.2.8 Compute \(\sum_{n=1}^\infty \left({3\over 5}\right)^n\). Each term is the sum of the previous two terms. Parametric equations, polar coordinates, and vector-valued functions Calculator-active practice: Parametric equations, polar coordinates, . A proof of the Integral Test is also given. Choose your answer to the question and click 'Continue' to see how you did. (answer), Ex 11.1.6 Determine whether \(\left\{{2^n\over n! 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. /BaseFont/SFGTRF+CMSL12 21 terms. endobj What if the interval is instead \([1,3/2]\)? /Filter /FlateDecode (answer). Determine whether the sequence converges or diverges. (answer), Ex 11.3.11 Find an \(N\) so that \(\sum_{n=1}^\infty {\ln n\over n^2}\) is between \(\sum_{n=1}^N {\ln n\over n^2}\) and \(\sum_{n=1}^N {\ln n\over n^2} + 0.005\). (answer), Ex 11.9.3 Find a power series representation for \( 2/(1-x)^3\). << endstream endobj 208 0 obj <. << Sequences can be thought of as functions whose domain is the set of integers. (answer), Ex 11.4.6 Approximate \(\sum_{n=1}^\infty (-1)^{n-1}{1\over n^4}\) to two decimal places. YesNo 2.(b). Most sections should have a range of difficulty levels in the problems although this will vary from section to section. Quiz 2: 8 questions Practice what you've learned, and level up on the above skills. At this time, I do not offer pdf's for . S.QBt'(d|/"XH4!qbnEriHX)Gs2qN/G jq8$$< /LastChar 127 Find the radius and interval of convergence for each series. (answer), Ex 11.2.9 Compute \(\sum_{n=1}^\infty {3^n\over 5^{n+1}}\). /FontDescriptor 23 0 R Determine whether each series converges absolutely, converges conditionally, or diverges. endobj Don't all infinite series grow to infinity? 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. 777.8 777.8] Which of the following is the 14th term of the sequence below? Series are sums of multiple terms. Ex 11.11.4 Show that \(\cos x\) is equal to its Taylor series for all \(x\) by showing that the limit of the error term is zero as N approaches infinity. 531.3 531.3 531.3] 531.3 531.3 531.3 295.1 295.1 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 Parametric Equations and Polar Coordinates, 9.5 Surface Area with Parametric Equations, 9.11 Arc Length and Surface Area Revisited, 10.7 Comparison Test/Limit Comparison Test, 12.8 Tangent, Normal and Binormal Vectors, 13.3 Interpretations of Partial Derivatives, 14.1 Tangent Planes and Linear Approximations, 14.2 Gradient Vector, Tangent Planes and Normal Lines, 15.3 Double Integrals over General Regions, 15.4 Double Integrals in Polar Coordinates, 15.6 Triple Integrals in Cylindrical Coordinates, 15.7 Triple Integrals in Spherical Coordinates, 16.5 Fundamental Theorem for Line Integrals, 3.8 Nonhomogeneous Differential Equations, 4.5 Solving IVP's with Laplace Transforms, 7.2 Linear Homogeneous Differential Equations, 8. << 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Ex 11.7.2 Compute \(\lim_{n\to\infty} |a_{n+1}/a_n|\) for the series \(\sum 1/n\). Chapter 10 : Series and Sequences. 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 MATH 126 Medians and Such. 70 terms. /Name/F2 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 Ex 11.7.4 Compute \(\lim_{n\to\infty} |a_n|^{1/n}\) for the series \(\sum 1/n\). /Subtype/Type1 Images. 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 >> (answer). /Filter[/FlateDecode] /BaseFont/VMQJJE+CMR8 Strip out the first 3 terms from the series \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{2^{ - n}}}}{{{n^2} + 1}}} \). 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. 777.8 444.4 444.4 444.4 611.1 777.8 777.8 777.8 777.8]