 9.4.1: Graphical Analysis The figures show the graphs of the first 10 term...
 9.4.2: Graphical Analysis The figures show the graphs of the first 10 term...
 9.4.3: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.4: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.5: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.6: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.7: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.8: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.9: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.10: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.11: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.12: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.13: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.14: In Exercises 314, use the Direct Comparison Test to determine the c...
 9.4.15: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.16: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.17: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.18: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.19: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.20: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.21: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.22: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.23: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.24: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.25: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.26: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.27: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.28: In Exercises 1528, use the Limit Comparison Test to determine the c...
 9.4.29: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.30: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.31: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.32: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.33: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.34: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.35: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.36: In Exercises 2936, test for convergence or divergence, using each t...
 9.4.37: Use the Limit Comparison Test with the harmonic series to show that...
 9.4.38: Prove that, if and are polynomials of degree and respectively, then...
 9.4.39: In Exercises 3942, use the polynomial test given in Exercise 38 to ...
 9.4.40: In Exercises 3942, use the polynomial test given in Exercise 38 to ...
 9.4.41: In Exercises 3942, use the polynomial test given in Exercise 38 to ...
 9.4.42: In Exercises 3942, use the polynomial test given in Exercise 38 to ...
 9.4.43: In Exercises 43 and 44, use the divergence test given in Exercise 3...
 9.4.44: In Exercises 43 and 44, use the divergence test given in Exercise 3...
 9.4.45: In Exercises 4548, determine the convergence or divergence of the s...
 9.4.46: In Exercises 4548, determine the convergence or divergence of the s...
 9.4.47: In Exercises 4548, determine the convergence or divergence of the s...
 9.4.48: In Exercises 4548, determine the convergence or divergence of the s...
 9.4.49: Review the results of Exercises 4548. Explain why careful analysis ...
 9.4.50: State the Direct Comparison Test and give an example of its use.
 9.4.51: State the Limit Comparison Test and give an example of its use.
 9.4.52: It appears that the terms of the series are less than the correspon...
 9.4.53: The figure shows the first 20 terms of the convergent series and th...
 9.4.54: Consider the series (a) Verify that the series converges. (b) Use a...
 9.4.55: True or False? In Exercises 5560, determine whether the statement i...
 9.4.56: True or False? In Exercises 5560, determine whether the statement i...
 9.4.57: True or False? In Exercises 5560, determine whether the statement i...
 9.4.58: True or False? In Exercises 5560, determine whether the statement i...
 9.4.59: True or False? In Exercises 5560, determine whether the statement i...
 9.4.60: True or False? In Exercises 5560, determine whether the statement i...
 9.4.61: Prove that if the nonnegative series and converge, then so does the...
 9.4.62: Use the result of Exercise 61 to prove that if the nonnegative seri...
 9.4.63: Find two series that demonstrate the result of Exercise 61.
 9.4.64: Find two series that demonstrate the result of Exercise 62.
 9.4.65: Suppose that and are series with positive terms. Prove that if and ...
 9.4.66: Suppose that and are series with positive terms. Prove that if and ...
 9.4.67: Use the result of Exercise 65 to show that each series converges.
 9.4.68: Use the result of Exercise 66 to show that each series diverges.
 9.4.69: Suppose that is a series with positive terms. Prove that if converg...
 9.4.70: Prove that the series converges.
 9.4.71: Is the infinite series convergent? Prove your statement.
 9.4.72: Prove that if is a convergent series of positive real numbers, then...
Solutions for Chapter 9.4: Comparisons of Series
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 9.4: Comparisons of Series
Get Full SolutionsSince 72 problems in chapter 9.4: Comparisons of Series have been answered, more than 84606 students have viewed full stepbystep solutions from this chapter. Chapter 9.4: Comparisons of Series includes 72 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981.

Complex fraction
See Compound fraction.

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

DMS measure
The measure of an angle in degrees, minutes, and seconds

Extracting square roots
A method for solving equations in the form x 2 = k.

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Logarithmic regression
See Natural logarithmic regression

Mean (of a set of data)
The sum of all the data divided by the total number of items

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Parameter
See Parametric equations.

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Slopeintercept form (of a line)
y = mx + b

Standard deviation
A measure of how a data set is spread

Terminal side of an angle
See Angle.

Vertical stretch or shrink
See Stretch, Shrink.

Whole numbers
The numbers 0, 1, 2, 3, ... .