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Math
Calculus
CALCULUS,EARLY TRANSCENTALS
Chapter 11.1, Problem 4DP
Chapter 11.1, Problem 4DP
BUY
CALCULUS,EARLY TRANSCENTALS
9th Edition
ISBN:
9780357114049
Author: Stewart
Publisher:
CENGAGE L
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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
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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
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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=n31
Problem 4E: List the first five terms of the sequence. 4. an=13n+1
Problem 5E: List the first five terms of the sequence. 5. 2n+nn2
Problem 6E: List the first five terms of the sequence. 6. n21n2+1n=3
Problem 7E: List the first five terms of the sequence. 7. an=(1)n1n2
Problem 8E: List the first five terms of the sequence. 8. an=(1)n4n
Problem 9E: List the first five terms of the sequence. 9. an=cosn
Problem 10E: List the first five terms of the sequence. 10. an=1+(1)n
Problem 11E: List the first five terms of the sequence. 11. an=(2)n(n+1)!
Problem 12E: List the first five terms of the sequence. 12. an=2n+1n!+1
Problem 13E: List the first five terms of the sequence. 13. a1=1,an+1=2an+1
Problem 14E: List the first five terms of the sequence. 10. a1 = 6, an+1=ann
Problem 15E: List the first five terms of the sequence. 11. a1 = 2, an+1=an1+an
Problem 16E: List the first five terms of the sequence. 12. a1 = 2, a2 = 1, an + 1 = an an 1
Problem 17E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few...
Problem 18E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few...
Problem 19E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few...
Problem 20E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few...
Problem 21E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few...
Problem 22E: Find a formula for the general term an of the sequence, assuming that the pattern of the first few...
Problem 23E: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the...
Problem 24E: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the...
Problem 25E: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the...
Problem 26E: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the...
Problem 27E: Determine whether the sequence converges or diverges. If it converges, find the limit. 27. an=5n+2
Problem 28E: Determine whether the sequence converges or diverges. If it converges, find the limit. 28. an=5n+2
Problem 29E: Determine whether the sequence converges or diverges. If it converges, find the limit. 29....
Problem 30E: Determine whether the sequence converges or diverges. If it converges, find the limit. 30....
Problem 31E: Determine whether sequence converges or diverges. If it converges, find the limit. 25. an=n4n32n
Problem 32E: Determine whether sequence converges or diverges. If it converges, find the limit. 26. an = 2 +...
Problem 33E: Determine whether sequence converges or diverges. If it converges, find the limit. 27. an = 3n7n
Problem 34E: Determine whether sequence converges or diverges. If it converges, find the limit. 28. an=3nn+2
Problem 35E: Determine whether sequence converges or diverges. If it converges, find the limit. 29. an=e1/n
Problem 36E: Determine whether sequence converges or diverges. If it converges, find the limit. 30. an=4n1+9n
Problem 37E: Determine whether sequence converges or diverges. If it converges, find the limit. 31. an=1+4n21+n2
Problem 38E: Determine whether sequence converges or diverges. If it converges, find the limit. 32. an=cos(nn+1)
Problem 39E: Determine whether sequence converges or diverges. If it converges, find the limit. 33. an=n2n3+4n
Problem 40E: Determine whether sequence converges or diverges. If it converges, find the limit. 34. an=e2n/(n+2)
Problem 41E: Determine whether sequence converges or diverges. If it converges, find the limit. 35. an=(1)n2n
Problem 42E: Determine whether sequence converges or diverges. If it converges, find the limit. 36. an=(1)n+1nn+n
Problem 43E: Determine whether sequence converges or diverges. If it converges, find the limit. 37....
Problem 44E: Determine whether sequence converges or diverges. If it converges, find the limit. 38. {1nn1n2n}
Problem 45E: Determine whether the sequence converges or diverges. If it converges, find the limit. 45. sinn
Problem 46E: Determine whether sequence converges or diverges. If it converges, find the limit. 40. an=tan1nn
Problem 47E: Determine whether sequence converges or diverges. If it converges, find the limit. 41. {n2en}
Problem 48E: Determine whether sequence converges or diverges. If it converges, find the limit. 42. an = 1n(n +...
Problem 49E: Determine whether sequence converges or diverges. If it converges, find the limit. 43. an=cos2n2n
Problem 50E: Determine whether sequence converges or diverges. If it converges, find the limit. 44. an=21+3nn
Problem 51E: Determine whether sequence converges or diverges. If it converges, find the limit. 45. an = n...
Problem 52E: Determine whether sequence converges or diverges. If it converges, find the limit. 46. an = 2ncos n
Problem 53E: Determine whether sequence converges or diverges. If it converges, find the limit. 47. an=(1+2n)n
Problem 54E: Determine whether sequence converges or diverges. If it converges, find the limit. 48. an=nn
Problem 55E: Determine whether sequence converges or diverges. If it converges, find the limit. 49. an = 1n(2n2 +...
Problem 56E: Determine whether sequence converges or diverges. If it converges, find the limit. 50. an=(1nn)2n
Problem 57E: Determine whether sequence converges or diverges. If it converges, find the limit. 51. an =...
Problem 58E: Determine whether sequence converges or diverges. If it converges, find the limit. 52. an=nn+1n+3
Problem 59E: Determine whether sequence converges or diverges. If it converges, find the limit. 53. {0, 1, 0, 0,...
Problem 60E: Determine whether sequence converges or diverges. If it converges, find the limit. 54....
Problem 61E: Determine whether sequence converges or diverges. If it converges, find the limit. 55. an=n!2n
Problem 62E: Determine whether sequence converges or diverges. If it converges, find the limit. 56. an=(3)nn!
Problem 63E: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the...
Problem 64E
Problem 65E: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the...
Problem 66E: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the...
Problem 67E
Problem 68E: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the...
Problem 69E
Problem 70E: (a) Determine whether the sequence defined as follows is convergent or divergent: a1 = 1 an + 1 = 4 ...
Problem 71E: If 1000 is invested at 6% interest, compounded annually, then after n years the investment is worth...
Problem 72E: If you deposit 100 at the end of every month into an account that pays 3% interest per year...
Problem 73E
Problem 74E
Problem 75E: For what values of r is the sequence {nrn} convergent?
Problem 76E: (a) If {an} is convergent, show that limnan+1=limnan (b) A sequence {an} is defined by a1 = 1 and...
Problem 77E: Suppose you know that {an} is a decreasing sequence and all its terms lie between the numbers 5 and...
Problem 78E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 79E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 80E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 81E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 82E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 83E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 84E: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?...
Problem 85E: Find the limit of the sequence {2,22,222,...}
Problem 86E: A sequence {an} is given by a1=2,an+1=2+an. (a) By induction or otherwise, show that {an} is...
Problem 87E: Show that the sequence defined by a1=1an+1=31an is increasing and an 3 for all n. Deduce that {an}...
Problem 88E: Show that the sequence defined by a1=2an+1=13an satisfies 0 an 2 and is decreasing. Deduce that...
Problem 89E: (a) Fibonacci posed the following problem: Suppose that rabbits live forever and that every month...
Problem 90E: (a) Let a1 = a, a2 = f(a), a3 = f(a2) = f(f(a)), . . . , an + 1 = f(an), where f is a continuous...
Problem 91E: (a) Use a graph to guess the value of the limit limnn5n! (b) Use a graph of the sequence in part (a)...
Problem 92E: Use Definition 2 directly to prove that limn rn = 0 when |r| 1.
Problem 93E: Prove Theorem 6. [Hint: Use either Definition 2 or the Squeeze Theorem.]
Problem 94E: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the...
Problem 95E: Prove that if limn an = 0 and {bn} is bounded, then limn (anbn) = 0.
Problem 96E: Let an=(1+1n)n. (a) Show that if 0 a b, then bn+1an+1ba(n+1)bn (b) Deduce that bn[(n + 1)a nb] ...
Problem 97E: Let a and b be positive numbers with a b. Let a1 be their arithmetic mean and b1 their geometric...
Problem 98E: (a) Show that if limn a2n = L and limn a2n+1 = L, then {an} is convergent and limn an = L. (b) If...
Problem 99E: The size of an undisturbed fish population has been modeled by the formula pn+1=bpna+pn where pn is...
Problem 1DP
Problem 2DP
Problem 3DP
Problem 4DP
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