/LastChar 127 stream 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 endobj (answer), Ex 11.1.4 Determine whether \(\left\{{n^2+1\over (n+1)^2}\right\}_{n=0}^{\infty}\) converges or diverges. /Name/F2 If youd like a pdf document containing the solutions the download tab above contains links to pdfs containing the solutions for the full book, chapter and section. 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 589.1 483.8 427.7 555.4 505 Free Practice Test Instructions: Choose your answer to the question and click 'Continue' to see how you did. Then we can say that the series diverges without having to do any extra work. Calculus II For Dummies Cheat Sheet - dummies Most sections should have a range of difficulty levels in the problems although this will vary from section to section. It turns out the answer is no. << Images. 9.8 Power Series Chapter 9 Sequences and Series Calculus II What is the radius of convergence? /FirstChar 0 If it converges, compute the limit. 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 endobj }\right\}_{n=0}^{\infty}\) converges or diverges. The Integral Test can be used on a infinite series provided the terms of the series are positive and decreasing. Which of the following sequences is NOT a geometric sequence? UcTIjeB#vog-TM'FaTzG(:k-BNQmbj}'?^h<=XgS/]o4Ilv%Jm >> We will examine Geometric Series, Telescoping Series, and Harmonic Series. You appear to be on a device with a "narrow" screen width (, 2.4 Equations With More Than One Variable, 2.9 Equations Reducible to Quadratic in Form, 4.1 Lines, Circles and Piecewise Functions, 1.5 Trig Equations with Calculators, Part I, 1.6 Trig Equations with Calculators, Part II, 3.6 Derivatives of Exponential and Logarithm Functions, 3.7 Derivatives of Inverse Trig Functions, 4.10 L'Hospital's Rule and Indeterminate Forms, 5.3 Substitution Rule for Indefinite Integrals, 5.8 Substitution Rule for Definite Integrals, 6.3 Volumes of Solids of Revolution / Method of Rings, 6.4 Volumes of Solids of Revolution/Method of Cylinders, A.2 Proof of Various Derivative Properties, A.4 Proofs of Derivative Applications Facts, 7.9 Comparison Test for Improper Integrals, 9. 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 12 0 obj xTn0+,ITi](N@ fH2}W"UG'.% Z#>y{!9kJ+ Which rule represents the nth term in the sequence 9, 16, 23, 30? 0 /Name/F5 Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. (5 points) Evaluate the integral: Z 1 1 1 x2 dx = SOLUTION: The function 1/x2 is undened at x = 0, so we we must evaluate the im- proper integral as a limit. Alternating Series Test For series of the form P ( 1)nb n, where b n is a positive and eventually decreasing sequence, then X ( 1)nb n converges ()limb n = 0 POWER SERIES De nitions X1 n=0 c nx n OR X1 n=0 c n(x a) n Radius of convergence: The radius is de ned as the number R such that the power series . (answer), Ex 11.2.3 Explain why \(\sum_{n=1}^\infty {3\over n}\) diverges. You may also use any of these materials for practice. 500 388.9 388.9 277.8 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 << Ex 11.7.5 \(\sum_{n=0}^\infty (-1)^{n}{3^n\over 5^n}\) (answer), Ex 11.7.6 \(\sum_{n=1}^\infty {n!\over n^n}\) (answer), Ex 11.7.7 \(\sum_{n=1}^\infty {n^5\over n^n}\) (answer), Ex 11.7.8 \(\sum_{n=1}^\infty {(n! Our mission is to provide a free, world-class education to anyone, anywhere. (answer), Ex 11.4.6 Approximate \(\sum_{n=1}^\infty (-1)^{n-1}{1\over n^4}\) to two decimal places. 979.2 489.6 489.6 489.6] All other trademarks and copyrights are the property of their respective owners. In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. We will also give many of the basic facts and properties well need as we work with sequences. 31 terms. Chapter 10 : Series and Sequences. Divergence Test. Legal. L7s[AQmT*Z;HK%H0yqt1r8 Level up on all the skills in this unit and collect up to 2000 Mastery points! Alternating Series Test - In this section we will discuss using the Alternating Series Test to determine if an infinite series converges or diverges. >> A ball is dropped from an unknown height (h) and it repeatedly bounces on the floor. /Subtype/Type1 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 Note as well that there really isnt one set of guidelines that will always work and so you always need to be flexible in following this set of guidelines. 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. (answer), Ex 11.1.6 Determine whether \(\left\{{2^n\over n! xu? ~k"xPeEV4Vcwww \ a:5d*%30EU9>,e92UU3Voj/$f BS!.eSloaY&h&Urm!U3L%g@'>`|$ogJ xYKs6W(MCG:9iIO=(lkFRI$x$AMN/" J?~i~d cXf9o/r.&Lxy%/D-Yt+"LX]Sfp]Xl-aM_[6(*~mQbh*28AjZx0 =||. A summary of all the various tests, as well as conditions that must be met to use them, we discussed in this chapter are also given in this section. (answer), Ex 11.2.5 Compute \(\sum_{n=0}^\infty {3\over 2^n}+ {4\over 5^n}\). Other sets by this creator. 665 570.8 924.4 812.6 568.1 670.2 380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 Calc II: Practice Final Exam 5 and our series converges because P nbn is a p-series with p= 4=3 >1: (b) X1 n=1 lnn n3 Set f(x) = lnx x3 and check that f0= 43x lnx+ x 4 <0 A Lot of Series Test Practice Problems - YouTube The chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al. Quiz 2: 8 questions Practice what you've learned, and level up on the above skills. Harmonic series and p-series. Complementary General calculus exercises can be found for other Textmaps and can be accessed here. /FontDescriptor 23 0 R >> << Strip out the first 3 terms from the series n=1 2n n2 +1 n = 1 2 n n 2 + 1. 413.2 531.3 826.4 295.1 354.2 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 At this time, I do not offer pdfs for solutions to individual problems. Calculus 2 | Math | Khan Academy 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 Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.