 8.4.1: If we know that lim kS_ ak = 1, then what can we say about a _ k = ...
 8.4.2: Is it true that if the terms of a series of positive terms decrease...
 8.4.3: Can the Integral Test be used to determine whether a series diverges?
 8.4.4: For what values of p does the series a _ k = 1 1 kp converge? For w...
 8.4.5: For what values of p does the series a _ k = 10 1 kp converge (init...
 8.4.6: Explain why the sequence of partial sums for a series with positive...
 8.4.7: Define the remainder of an infinite series.
 8.4.8: If a series of positive terms converges, does it follow that the re...
 8.4.9: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.10: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.11: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.12: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.13: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.14: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.15: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.16: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.17: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.18: 918. Divergence Test Use the Divergence Test to determine whether t...
 8.4.19: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.20: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.21: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.22: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.23: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.24: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.25: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.26: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.27: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.28: 1928. Integral Test Use the Integral Test to determine the converge...
 8.4.29: 2934. pseries Determine the convergence or divergence of the follo...
 8.4.30: 2934. pseries Determine the convergence or divergence of the follo...
 8.4.31: 2934. pseries Determine the convergence or divergence of the follo...
 8.4.32: 2934. pseries Determine the convergence or divergence of the follo...
 8.4.33: 2934. pseries Determine the convergence or divergence of the follo...
 8.4.34: 2934. pseries Determine the convergence or divergence of the follo...
 8.4.35: 3542. Remainders and estimates Consider the following convergent se...
 8.4.36: 3542. Remainders and estimates Consider the following convergent se...
 8.4.37: 3542. Remainders and estimates Consider the following convergent se...
 8.4.38: 3542. Remainders and estimates Consider the following convergent se...
 8.4.39: 3542. Remainders and estimates Consider the following convergent se...
 8.4.40: 3542. Remainders and estimates Consider the following convergent se...
 8.4.41: 3542. Remainders and estimates Consider the following convergent se...
 8.4.42: 3542. Remainders and estimates Consider the following convergent se...
 8.4.43: 4350. Properties of series Use the properties of infinite series to...
 8.4.44: 4350. Properties of series Use the properties of infinite series to...
 8.4.45: 4350. Properties of series Use the properties of infinite series to...
 8.4.46: 4350. Properties of series Use the properties of infinite series to...
 8.4.47: 4350. Properties of series Use the properties of infinite series to...
 8.4.48: 4350. Properties of series Use the properties of infinite series to...
 8.4.49: 4350. Properties of series Use the properties of infinite series to...
 8.4.50: 4350. Properties of series Use the properties of infinite series to...
 8.4.51: Explain why or why not Determine whether the following statements a...
 8.4.52: 5257. Choose your test Determine whether the following series conve...
 8.4.53: 5257. Choose your test Determine whether the following series conve...
 8.4.54: 5257. Choose your test Determine whether the following series conve...
 8.4.55: 5257. Choose your test Determine whether the following series conve...
 8.4.56: 5257. Choose your test Determine whether the following series conve...
 8.4.57: 5257. Choose your test Determine whether the following series conve...
 8.4.58: Log pseries Consider the series a _ k = 2 1 k1ln k2p, where p is a...
 8.4.59: Loglog pseries Consider the series a _ k = 3 1 k 1ln k21ln ln k2p,...
 8.4.60: Find a series Find a series that a. converges faster than a 1 k2 bu...
 8.4.61: A divergence proof Give an argument similar to that given in the te...
 8.4.62: Properties proof Use the ideas in the proof of Property 1 of Theore...
 8.4.63: Property of divergent series Prove that if aak diverges, then acak ...
 8.4.64: Prime numbers The prime numbers are those positive integers that ar...
 8.4.65: The zeta function The Riemann zeta function is the subject of exten...
 8.4.66: Showing that a H k_1 1 k2 _ P2 6 In 1734, Leonhard Euler informally...
 8.4.67: Reciprocals of odd squares Assume that a _ k = 1 1 k2 = p2 6 (Exerc...
 8.4.68: Shifted pseries Consider the sequence 5Fn6 defined by Fn = a _ k =...
 8.4.69: A sequence of sums Consider the sequence 5xn6 defined for n = 1, 2,...
 8.4.70: The harmonic series and Eulers constant a. Sketch the function f 1x...
 8.4.71: Stacking dominoes Consider a set of identical dominoes that are 2 i...
 8.4.72: Gabriels wedding cake Consider a wedding cake of infinite height, e...
 8.4.73: The harmonic series and the Fibonacci sequence The Fibonacci sequen...
Solutions for Chapter 8.4: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 8.4
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Since 73 problems in chapter 8.4 have been answered, more than 57371 students have viewed full stepbystep solutions from this chapter. Chapter 8.4 includes 73 full stepbystep solutions.

Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Cube root
nth root, where n = 3 (see Principal nth root),

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Directed angle
See Polar coordinates.

Focal length of a parabola
The directed distance from the vertex to the focus.

Future value of an annuity
The net amount of money returned from an annuity.

Horizontal component
See Component form of a vector.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Index
See Radical.

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Matrix element
Any of the real numbers in a matrix

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Third quartile
See Quartile.