 10.5.1: In the Ratio Test, is equal to lim n an+1 an or lim n an an+1 ?
 10.5.2: Is the Ratio Test conclusive for n=1 1 2n ? Is it conclusive for n=...
 10.5.3: Can the Ratio Test be used to show convergence if the series is onl...
 10.5.4: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.5: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.6: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.7: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.8: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.9: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.10: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.11: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.12: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.13: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.14: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.15: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.16: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.17: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.18: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.19: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.20: In Exercises 120, apply the Ratio Test to determine convergence or ...
 10.5.21: Show that n=1 nk 3n converges for all exponents k.
 10.5.22: Show that n=1 n2xn converges if x < 1.
 10.5.23: Show that n=1 2nxn converges if x < 1 2 .
 10.5.24: Show that n=1 rn n! converges for all r.
 10.5.25: Show that n=1 rn n converges if r < 1.
 10.5.26: Is there any value of k such that n=1 2n nk converges?
 10.5.27: Show that n=1 n! nn converges. Hint: Use lim n 1 + 1 n n = e.
 10.5.28: In Exercises 2833, assume that an+1/an converges to = 1 3 . What ...
 10.5.29: In Exercises 2833, assume that an+1/an converges to = 1 3 . What ...
 10.5.30: In Exercises 2833, assume that an+1/an converges to = 1 3 . What ...
 10.5.31: In Exercises 2833, assume that an+1/an converges to = 1 3 . What ...
 10.5.32: In Exercises 2833, assume that an+1/an converges to = 1 3 . What ...
 10.5.33: In Exercises 2833, assume that an+1/an converges to = 1 3 . What ...
 10.5.34: Assume that an+1/an converges to = 4. Does n=1 a1 n converge (assum...
 10.5.35: Is the Ratio Test conclusive for the pseries n=1 1 np ?
 10.5.36: In Exercises 3641, use the Root Test to determine convergence or di...
 10.5.37: In Exercises 3641, use the Root Test to determine convergence or di...
 10.5.38: In Exercises 3641, use the Root Test to determine convergence or di...
 10.5.39: In Exercises 3641, use the Root Test to determine convergence or di...
 10.5.40: In Exercises 3641, use the Root Test to determine convergence or di...
 10.5.41: In Exercises 3641, use the Root Test to determine convergence or di...
 10.5.42: Prove that n=1 2n2 n! diverges. Hint: Use 2n2 = (2n)n and n! nn.
 10.5.43: In Exercises 4362, determine convergence or divergence using any me...
 10.5.44: In Exercises 4362, determine convergence or divergence using any me...
 10.5.45: In Exercises 4362, determine convergence or divergence using any me...
 10.5.46: In Exercises 4362, determine convergence or divergence using any me...
 10.5.47: In Exercises 4362, determine convergence or divergence using any me...
 10.5.48: In Exercises 4362, determine convergence or divergence using any me...
 10.5.49: In Exercises 4362, determine convergence or divergence using any me...
 10.5.50: In Exercises 4362, determine convergence or divergence using any me...
 10.5.51: In Exercises 4362, determine convergence or divergence using any me...
 10.5.52: In Exercises 4362, determine convergence or divergence using any me...
 10.5.53: In Exercises 4362, determine convergence or divergence using any me...
 10.5.54: In Exercises 4362, determine convergence or divergence using any me...
 10.5.55: In Exercises 4362, determine convergence or divergence using any me...
 10.5.56: In Exercises 4362, determine convergence or divergence using any me...
 10.5.57: In Exercises 4362, determine convergence or divergence using any me...
 10.5.58: In Exercises 4362, determine convergence or divergence using any me...
 10.5.59: In Exercises 4362, determine convergence or divergence using any me...
 10.5.60: In Exercises 4362, determine convergence or divergence using any me...
 10.5.61: In Exercises 4362, determine convergence or divergence using any me...
 10.5.62: In Exercises 4362, determine convergence or divergence using any me...
 10.5.63: Proof of the Root Test Let S = n=0 an be a positive series, and ass...
 10.5.64: Show that the Ratio Test does not apply, but verify convergence usi...
 10.5.65: Let S = n=1 cnn! nn , where c is a constant. (a) Prove that S conve...
Solutions for Chapter 10.5: The Ratio and Root Tests and Strategies for Choosing Tests
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 10.5: The Ratio and Root Tests and Strategies for Choosing Tests
Get Full SolutionsSince 65 problems in chapter 10.5: The Ratio and Root Tests and Strategies for Choosing Tests have been answered, more than 40740 students have viewed full stepbystep solutions from this chapter. Chapter 10.5: The Ratio and Root Tests and Strategies for Choosing Tests includes 65 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: Early Transcendentals , edition: 3. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Absolute value of a vector
See Magnitude of a vector.

Arccosecant function
See Inverse cosecant function.

Arctangent function
See Inverse tangent function.

Circle graph
A circular graphical display of categorical data

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Differentiable at x = a
ƒ'(a) exists

Divergence
A sequence or series diverges if it does not converge

End behavior asymptote of a rational function
A polynomial that the function approaches as.

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

Inductive step
See Mathematical induction.

Instantaneous rate of change
See Derivative at x = a.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Inverse function
The inverse relation of a onetoone function.

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Third quartile
See Quartile.

Zero vector
The vector <0,0> or <0,0,0>.