T Diagnostic Tests 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 Infinite Sequences And Series 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 H Complex Numbers 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 Chapter Questions expand_more
Problem 1E: (a) What is a sequence? (b) What does it mean to say that limn an = 8? (c) What does it mean to say... Problem 2E: (a) What is a convergent sequence? Give two examples. (b) What is a divergent sequence ? Give two... Problem 3E: List the first five terms of the sequence. 3. an=2n2n+1 Problem 4E: List the first five terms of the sequence. 4. an=n21n2+1 Problem 5E: List the first five terms of the sequence. 5. an=(1)n15n Problem 6E: List the first five terms of the sequence. 6. an=cosn2 Problem 7E: List the first five terms of the sequence. 7. an=1(n+1)! Problem 8E: List the first five terms of the sequence. 8. an=(1)nnn!+1 Problem 9E Problem 10E: List the first five terms of the sequence. 10. a1 = 6, an+1=ann Problem 11E: List the first five terms of the sequence. 11. a1 = 2, an+1=an1+an Problem 12E: List the first five terms of the sequence. 12. a1 = 2, a2 = 1, an+1 = an an1 Problem 13E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few... Problem 14E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few... Problem 15E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few... Problem 16E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few... Problem 17E Problem 18E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few... Problem 19E: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the... Problem 20E: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the... Problem 21E Problem 22E Problem 23E: Determine whether the sequence converges or diverges. If it converges, find the limit. 23.... Problem 24E: Determine whether the sequence converges or diverges. If it converges, find the limit. 24.... Problem 25E: Determine whether the sequence converges or diverges. If it converges, find the limit. 25. an=n4n32n Problem 26E: Determine whether the sequence converges or diverges. If it converges, find the limit. 26. an = 2 +... Problem 27E Problem 28E: Determine whether the sequence converges or diverges. If it converges, find the limit. 28. an=3nn+2 Problem 29E Problem 30E: Determine whether the sequence converges or diverges. If it converges, find the limit. 30. an=4n1+9n Problem 31E Problem 32E: Determine whether the sequence converges or diverges. If it converges, find the limit. 32.... Problem 33E Problem 34E Problem 35E Problem 36E: Determine whether the sequence converges or diverges. If it converges, find the limit. 36.... Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E: Determine whether the sequence converges or diverges. If it converges, find the limit. 42. an = ln(n... Problem 43E: Determine whether the sequence converges or diverges. If it converges, find the limit. 43.... Problem 44E Problem 45E Problem 46E: Determine whether the sequence converges or diverges. If it converges, find the limit. 46. an = 2n... Problem 47E Problem 48E: Determine whether the sequence converges or diverges. If it converges, find the limit. 48. an=nn Problem 49E: Determine whether the sequence converges or diverges. If it converges, find the limit. 49. an =... Problem 50E: Determine whether the sequence converges or diverges. If it converges, find the limit. 50.... Problem 51E: Determine whether the sequence converges or diverges. If it converges, find the limit. 51. an =... Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E: If you deposit 100 at the end of every month into an account that pays 3% interest per year... Problem 67E: A fish farmer has 5000 catfish in his pond. The number of catfish increases by 8% per month and the... Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?... Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E: Show that the sequence defined by a1=1an+1=31an is increasing and an 3 for all n. Deduce that {an}... Problem 82E Problem 83E: (a) Fibonacci posed the following problem: Suppose that rabbits live forever and that every month... Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E: Prove Theorem 7. Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E: The size of an undisturbed fish population has been modeled by the formula pn+1=bpna+pn where pn is... format_list_bulleted