 11.8.1: What is a power series?
 11.8.2: (a) What is the radius of convergence of a power series? How do you...
 11.8.3: Find the radius of convergence and interval of convergence of the s...
 11.8.4: Find the radius of convergence and interval of convergence of the s...
 11.8.5: Find the radius of convergence and interval of convergence of the s...
 11.8.6: Find the radius of convergence and interval of convergence of the s...
 11.8.7: Find the radius of convergence and interval of convergence of the s...
 11.8.8: Find the radius of convergence and interval of convergence of the s...
 11.8.9: Find the radius of convergence and interval of convergence of the s...
 11.8.10: Find the radius of convergence and interval of convergence of the s...
 11.8.11: Find the radius of convergence and interval of convergence of the s...
 11.8.12: Find the radius of convergence and interval of convergence of the s...
 11.8.13: Find the radius of convergence and interval of convergence of the s...
 11.8.14: Find the radius of convergence and interval of convergence of the s...
 11.8.15: Find the radius of convergence and interval of convergence of the s...
 11.8.16: Find the radius of convergence and interval of convergence of the s...
 11.8.17: Find the radius of convergence and interval of convergence of the s...
 11.8.18: Find the radius of convergence and interval of convergence of the s...
 11.8.19: Find the radius of convergence and interval of convergence of the s...
 11.8.20: Find the radius of convergence and interval of convergence of the s...
 11.8.21: Find the radius of convergence and interval of convergence of the s...
 11.8.22: Find the radius of convergence and interval of convergence of the s...
 11.8.23: Find the radius of convergence and interval of convergence of the s...
 11.8.24: Find the radius of convergence and interval of convergence of the s...
 11.8.25: Find the radius of convergence and interval of convergence of the s...
 11.8.26: Find the radius of convergence and interval of convergence of the s...
 11.8.27: Find the radius of convergence and interval of convergence of the s...
 11.8.28: Find the radius of convergence and interval of convergence of the s...
 11.8.29: If is convergent, does it follow that the following series are conv...
 11.8.30: Suppose that converges when and diverges when . What can be said ab...
 11.8.31: If is a positive integer, find the radius of convergence of the series
 11.8.32: Let and be real numbers with . Find a power series whose interval o...
 11.8.33: Is it possible to find a power series whose interval of convergence...
 11.8.34: Graph the first several partial sums of the series , together with ...
 11.8.35: The function defined by is called the Bessel function of order 1. (...
 11.8.36: The function defined by is called an Airy function after the Englis...
 11.8.37: A function is defined by that is, its coefficients are and for all ...
 11.8.38: If , where for all , find the interval of convergence of the series...
 11.8.39: Show that if , where , then the radius of convergence of the power ...
 11.8.40: Suppose that the power series satisfies for all . Show that if exis...
 11.8.41: Suppose the series has radius of convergence 2 and the series has r...
 11.8.42: Suppose that the radius of convergence of the power series is . Wha...
Solutions for Chapter 11.8: POWER SERIES
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 11.8: POWER SERIES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Since 42 problems in chapter 11.8: POWER SERIES have been answered, more than 21919 students have viewed full stepbystep solutions from this chapter. Chapter 11.8: POWER SERIES includes 42 full stepbystep solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Binomial
A polynomial with exactly two terms

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Commutative properties
a + b = b + a ab = ba

End behavior
The behavior of a graph of a function as.

Geometric series
A series whose terms form a geometric sequence.

Inductive step
See Mathematical induction.

Leaf
The final digit of a number in a stemplot.

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Open interval
An interval that does not include its endpoints.

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

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

Standard form of a complex number
a + bi, where a and b are real numbers

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Sum of an infinite series
See Convergence of a series

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

Xmin
The xvalue of the left side of the viewing window,.