1 Functions And Models 2 Limits And Derivatives 3 Differentiation Rules 4 Applications Of Differentiation 5 Integrals 6 Applications Of Integration 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Sequences, Series, And Power Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G The Logarithm Defined As An Integral 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 And Absolute Convergence 11.6 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 Chapter Questions expand_more
Problem 1E: (a) What is the difference between a sequence and a series? (b) What is a convergent series? What is... Problem 2E: Explain what it means to say that n=1an=5. Problem 3E: Calculate the sum of the seriesn=1an whose partial sums are given. 3. sn = 2 3(0.8)n Problem 4E: Calculate the sum of the seriesn=1an whose partial sums are given. 4. 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: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does... Problem 8E: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does... Problem 9E Problem 10E Problem 11E 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: Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of... Problem 15E: Let an=2n3n+1 (a) Determine whether {an} is convergent. (b) Determine whether n=1an is convergent. Problem 16E: (a) Explain the difference between i=1naiandj=1naj (b) Explain the difference between... Problem 17E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in... Problem 18E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in... Problem 19E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in... Problem 20E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in... Problem 21E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in... Problem 22E: Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in... Problem 23E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 24E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 25E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 26E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 27E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 28E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 29E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 30E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 31E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 32E: Determine whether the geometric series is convergent or divergent. If it is convergent, find its... Problem 33E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 27.... Problem 34E Problem 35E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 35.... Problem 36E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 28.... Problem 37E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 29.... Problem 38E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 30.... Problem 39E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 31.... Problem 40E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 32.... Problem 41E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 33.... Problem 42E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 34.... Problem 43E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 35.... Problem 44E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 36.... Problem 45E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 37.... Problem 46E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 38.... Problem 47E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 39.... Problem 48E Problem 49E: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 49.... Problem 50E Problem 51E: Let X = 0.99999 .... (a) Do you think that x 1 or x = 1? (b) Sum a geometric series to find the... Problem 52E Problem 53E: Express the number as a ratio of integers. 51. 0.8=0.8888... Problem 54E: Express the number as a ratio of integers. 52. 0.46=0.46464646... Problem 55E: Express the number as a ratio of integers. 53. 2.516=2.516516516... Problem 56E Problem 57E: Express the number as a ratio of integers. 55. 1.234567 Problem 58E Problem 59E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 60E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 61E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 62E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 63E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 64E Problem 65E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 66E: Find the values of x for which the series converges. Find the sum of the series for those values of... Problem 67E Problem 68E: Use the partial fraction command on a computer algebra system to find a convenient expression for... Problem 69E: If the nth partial sum of a series n=1an is sn=n1n+1 find an. and n=1an Problem 70E: If the nth partial sum of a series n=1an is sn = 3 - n2n, find an and n=1an . Problem 71E: A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each... Problem 72E: A patient is injected with a drug every 12 hours. Immediately before each injection the... Problem 73E: A patient takes 150 mg of a drug at the same time every day. Just before each tablet is taken, 5% of... Problem 74E: After injection of a dose D of insulin, the concentration of insulin in a patients system decays... Problem 75E: When money is spent on goods and services, those who receive the money also spend some of it. The... Problem 76E: A certain ball has the property that each time it falls from a height h onto a hard, level surface,... Problem 77E: Find the value of c if n=2(1+c)n=2 Problem 78E: Find the value of c such that n=0enc=10 Problem 79E Problem 80E Problem 81E Problem 82E: Graph the curves y = xn, 0 x 1, for n = 0, 1, 2, 3, 4, ... on a common screen. By finding the... Problem 83E: The figure shows two circles C and D of radius 1 that touch at P. The line T is a common tangent... Problem 84E Problem 85E: What is wrong with the following calculation?... Problem 86E Problem 87E Problem 88E: If an is divergent and c 0, show that can, is divergent. Problem 89E Problem 90E Problem 91E Problem 92E: The Fibonacci sequence was defined in Section 11.1 by the equations f1=1, f2=1, fn=fn1+fn2 n3 Show... Problem 93E: The Cantor set, named after the German mathematician Georg Cantor (18451918), is constructed as... Problem 94E: (a) A sequence an is defined recursively by the equation an=12an1+an2 for n3 , where a1 and a2 can... Problem 95E: Consider the series n=1n/(n+1)!. (a) Find the partial sums s1, s2, s3, and s4. Do you recognize the... Problem 96E: In the figure at the right there are infinitely many circles approaching the vertices of an... format_list_bulleted
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