 9.6.1: Verifying a Formula In Exercises 14, verify the formula.
 9.6.2: Verifying a Formula In Exercises 14, verify the formula.
 9.6.3: Verifying a Formula In Exercises 14, verify the formula.
 9.6.4: Verifying a Formula In Exercises 14, verify the formula.
 9.6.5: Matching In Exercises 510, match the series with the graph of its s...
 9.6.6: Matching In Exercises 510, match the series with the graph of its s...
 9.6.7: Matching In Exercises 510, match the series with the graph of its s...
 9.6.8: Matching In Exercises 510, match the series with the graph of its s...
 9.6.9: Matching In Exercises 510, match the series with the graph of its s...
 9.6.10: Matching In Exercises 510, match the series with the graph of its s...
 9.6.11: Numerical, Graphical, and Analytic Analysis In Exercises 11 and 12,...
 9.6.12: Numerical, Graphical, and Analytic Analysis In Exercises 11 and 12,...
 9.6.13: Using the Ratio Test In Exercises 1334, use the Ratio Test to deter...
 9.6.14: Using the Ratio Test In Exercises 1334, use the Ratio Test to deter...
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 9.6.27: Using the Ratio Test In Exercises 1334, use the Ratio Test to deter...
 9.6.28: Using the Ratio Test In Exercises 1334, use the Ratio Test to deter...
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 9.6.33: Using the Ratio Test In Exercises 1334, use the Ratio Test to deter...
 9.6.34: Using the Ratio Test In Exercises 1334, use the Ratio Test to deter...
 9.6.35: Using the Root Test In Exercises 3550, use the Root Test to determi...
 9.6.36: Using the Root Test In Exercises 3550, use the Root Test to determi...
 9.6.37: Using the Root Test In Exercises 3550, use the Root Test to determi...
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 9.6.48: Using the Root Test In Exercises 3550, use the Root Test to determi...
 9.6.49: Using the Root Test In Exercises 3550, use the Root Test to determi...
 9.6.50: Using the Root Test In Exercises 3550, use the Root Test to determi...
 9.6.51: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.52: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.53: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.54: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.55: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.56: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.57: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.58: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.59: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.60: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.61: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.62: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.63: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.64: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.65: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.66: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.67: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.68: Determining Convergence or Divergence In Exercises 5168, determine ...
 9.6.69: Identifying Series In Exercises 6972, identify the two series that ...
 9.6.70: Identifying Series In Exercises 6972, identify the two series that ...
 9.6.71: Identifying Series In Exercises 6972, identify the two series that ...
 9.6.72: Identifying Series In Exercises 6972, identify the two series that ...
 9.6.73: Writing an Equivalent Series In Exercises 73 and 74, write an equiv...
 9.6.74: Writing an Equivalent Series In Exercises 73 and 74, write an equiv...
 9.6.75: Finding the Number of Terms In Exercises 75 and 76, (a) determine t...
 9.6.76: Finding the Number of Terms In Exercises 75 and 76, (a) determine t...
 9.6.77: Using a Recursively Defined Series In Exercises 7782, the terms of ...
 9.6.78: Using a Recursively Defined Series In Exercises 7782, the terms of ...
 9.6.79: Using a Recursively Defined Series In Exercises 7782, the terms of ...
 9.6.80: Using a Recursively Defined Series In Exercises 7782, the terms of ...
 9.6.81: Using a Recursively Defined Series In Exercises 7782, the terms of ...
 9.6.82: Using a Recursively Defined Series In Exercises 7782, the terms of ...
 9.6.83: Using the Ratio Test or Root Test In Exercises 83 86, use the Ratio...
 9.6.84: Using the Ratio Test or Root Test In Exercises 83 86, use the Ratio...
 9.6.85: Using the Ratio Test or Root Test In Exercises 83 86, use the Ratio...
 9.6.86: Using the Ratio Test or Root Test In Exercises 83 86, use the Ratio...
 9.6.87: Finding Values In Exercises 8792, find the values of for which the ...
 9.6.88: Finding Values In Exercises 8792, find the values of for which the ...
 9.6.89: Finding Values In Exercises 8792, find the values of for which the ...
 9.6.90: Finding Values In Exercises 8792, find the values of for which the ...
 9.6.91: Finding Values In Exercises 8792, find the values of for which the ...
 9.6.92: Finding Values In Exercises 8792, find the values of for which the ...
 9.6.93: Ratio Test State the Ratio Test.
 9.6.94: Root Test State the Root Test.
 9.6.95: Think About It You are told that the terms of a positive series app...
 9.6.96: Think About It What can you conclude about the convergence or diver...
 9.6.97: Using an Alternating Series Using the Ratio Test, it is determined ...
 9.6.98: HOW DO YOU SEE IT? The figure shows the first 10 terms of the conve...
 9.6.99: Proof Prove Property 2 of Theorem 9.17.
 9.6.100: Proof Prove Theorem 9.18. (Hint for Property 1: If the limit equals...
 9.6.101: Verifying an Inconclusive Test In Exercises 101104, verify that the...
 9.6.102: Verifying an Inconclusive Test In Exercises 101104, verify that the...
 9.6.103: Verifying an Inconclusive Test In Exercises 101104, verify that the...
 9.6.104: Verifying an Inconclusive Test In Exercises 101104, verify that the...
 9.6.105: Verifying an Inconclusive Test Show that the Root Test is inconclus...
 9.6.106: Verifying Inconclusive Tests Show that the Ratio Test and the Root ...
 9.6.107: Using Values Determine the convergence or divergence of the series ...
 9.6.108: Using a Series Show that if is absolutely convergent, then
 9.6.109: Show that if the series converges, then the series converges also.
 9.6.110: Is the following series convergent or divergent?
Solutions for Chapter 9.6: The Ratio and Root Tests
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 9.6: The Ratio and Root Tests
Get Full SolutionsSince 110 problems in chapter 9.6: The Ratio and Root Tests have been answered, more than 43705 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. Chapter 9.6: The Ratio and Root Tests includes 110 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6.

Census
An observational study that gathers data from an entire population

Complex fraction
See Compound fraction.

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Direction angle of a vector
The angle that the vector makes with the positive xaxis

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Focus, foci
See Ellipse, Hyperbola, Parabola.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Horizontal shrink or stretch
See Shrink, stretch.

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Orthogonal vectors
Two vectors u and v with u x v = 0.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Rational zeros
Zeros of a function that are rational numbers.

Real number
Any number that can be written as a decimal.

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.

Time plot
A line graph in which time is measured on the horizontal axis.