1 Functions And Limits 2 Derivatives 3 Applications Of Differentiation 4 Integrals 5 Applications Of Integration 6 Inverse Functions 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Infinite Sequences And Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus 17 Second-order Differential Equations expand_more
11.1 Sequences 11.2 Series 11.3 The Integral Test And Estimates Of Sums 11.4 The Comparison Tests 11.5 Alternating Series 11.6 Absolute Convergence And The Ratio And Root Tests 11.7 Strategy For Testing Series 11.8 Power Series 11.9 Representations Of Functions As Power Series 11.10 Taylor And Maclaurin Series 11.11 Applications Of Taylor Polynomials 11.R Review 11.P Problem Plus expand_more
Problem 1E: a What is the difference between a sequence and a series? b What is the convergent series? What is a... Problem 2E: Explain what it means to say that n=1an=5. Problem 3E: Calculate the sum of the series n=1an whose partial sums are given. sn=23(0.8)n Problem 4E: Calculate the sum of the series n=1an whose partial sums are given. sn=n214n2+1 Problem 5E Problem 6E: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does... Problem 7E Problem 8E: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does... Problem 9E: Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of... Problem 10E: Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of... Problem 11E: Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of... Problem 12E: Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of... Problem 13E: Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of... Problem 14E Problem 15E: Let an=2n3n+1. a Determine whether {an} is convergent. b Determine whether n=1an is convergent. Problem 16E Problem 17E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 18E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 19E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 20E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 21E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 22E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 23E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 24E Problem 25E Problem 26E Problem 27E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 28E Problem 29E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 30E Problem 31E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 32E Problem 33E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. n=114+en Problem 34E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 35E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 36E Problem 37E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 38E Problem 39E Problem 40E Problem 41E: Determine whether the series is convergent or divergent. If it is convergent, find its sum.... Problem 42E Problem 43E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum as in... Problem 44E Problem 45E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum as in... Problem 46E Problem 47E Problem 48E Problem 49E: Let x=0.99999.... a Do you think that x1 or x=1? b Sum a geometric series to find the value of x. c... Problem 50E Problem 51E: Express the number as a ratio of integers. 0.8=0.8888... Problem 52E: Express the number as a ratio of integers. 0.46=0.46464646.. Problem 53E: Express the number as a ratio of integers. 0.516=0.516516516... Problem 54E: Express the number as a ratio of integers. 10.135=10.135353535... Problem 55E: Express the number as a ratio of integers. 1.234567 Problem 56E: Express the number as a ratio of integers. 5.71358 Problem 57E Problem 58E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E: Use the partial fraction command on your CAS to find a convenient expression for the partial sum,... Problem 66E Problem 67E: If the nth partial sum of a series n=1an is Sn=n1n+1 find an and n=1an. Problem 68E: If the nth partial sum of a series n=1an is sn=3n2n, find an and n=1an. Problem 69E: A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each... Problem 70E Problem 71E: A patient takes 150 mg of a drug at the same time every day. Just before each tablet is taken, 5 of... Problem 72E Problem 73E: When money is spent on goods and services, those who receive the money also spend some of it. The... Problem 74E: A certain ball has the property that each time it falls from a height h onto a hard, level surface,... Problem 75E: Find the value of c if n=2(1+c)n=2 Problem 76E: Find the value of c such that n=0enc=10 Problem 77E: In Example 9 we showed that the harmonic series is divergent. Here we outline another method, making... Problem 78E: Graph the curves y=xn, 0x1, for n=0,1,2,3,4,... on a common screen. By finding the areas between... Problem 79E Problem 80E Problem 81E: What is wrong with the following calculation? 0=0+0+0+... =(11)+(11)+(11)+... =11+11+11+...... Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E: If an and bn are both divergent, is (an+bn) necessarily divergent? Problem 87E Problem 88E: The Fibonacci sequence was defined in Section 11.1 by the equations f1=1, f2=1, fn=fn1+fn2 n3 Show... Problem 89E: The Cantor set, named after the German mathematician Georg Cantor 18451918, is constructed as... Problem 90E Problem 91E: Consider the series n=1nn+1!. a Find the partial sums S1, S2, S3, and S4. Do you recognize the... Problem 92E: In the figure at the right there are infinitely many circles approaching the vertices of an... format_list_bulleted