 3.2.1: For xn given by the following formulas, establish either the conver...
 3.2.2: Give an example of two divergent sequences X and Y such that: ) (a)...
 3.2.3: Show that if X and Y are sequences such that X and X + Y are conver...
 3.2.4: Show that if X and Y are sequences such that X converges to x =1= 0...
 3.2.5: Show that the following sequences are not convergent. (a) (2n), (b)...
 3.2.6: Find the limits of the following sequences: (a) lim(2+1/n)2). (b) l...
 3.2.7: If (b ) isaboundedsequence and lim(a ) = 0, show that lim(a b ) = o...
 3.2.8: Explain why the result in equation (3) before Theorem 3.2.4 cannot ...
 3.2.9: Let Yn := .Jm  Jii for n EN. Show that (Yn) and (JiiYn) converge. ...
 3.2.10: Determine the following limits. (a) lim(3Jii)1/2n), (b) lim(n + l)l...
 3.2.11: If 0 < a < b, determine lim an + bn ) . 1
 3.2.12: If a > 0, b > 0, showthat lim (v'(n + a)(n + b)  n) = (a + b)/
 3.2.13: U~ethe SqueezeTheorem3.2.7to determinethe limitsof the following. (...
 3.2.14: Show that if zn := (an + bn)l/n where 0 < a < b, then lim(z n) = b....
 3.2.15: Apply Theorem 3.2;11 to the following sequences, where a, b satisfy...
 3.2.16: (a) Give an example of a convergent sequence (xn) of positive numbe...
 3.2.17: Let X = (xn) be a sequenceof positivereal numberssuch that lim(xn+1...
 3.2.18: Discuss the convergence of the following sequences, where a, b sati...
 3.2.19: Let (xn) be a sequence of positive real numbers such that lim(x~/n)...
 3.2.20: (a) Give an example of a convergent sequence (xn) of positive numbe...
 3.2.21: (Thus, this property cannot be used as a test for convergence.) 2
 3.2.22: Suppose that (xn) is a convergent sequence and (Yn) is such that fo...
 3.2.23: Showthat if (xn)and (yn) are convergentsequences,then the sequences...
Solutions for Chapter 3.2: Limit Theorems
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 3.2: Limit Theorems
Get Full SolutionsChapter 3.2: Limit Theorems includes 23 full stepbystep solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Since 23 problems in chapter 3.2: Limit Theorems have been answered, more than 8172 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484.

Addition property of inequality
If u < v , then u + w < v + w

Convenience sample
A sample that sacrifices randomness for convenience

Descriptive statistics
The gathering and processing of numerical information

Direction vector for a line
A vector in the direction of a line in threedimensional space

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

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Irrational numbers
Real numbers that are not rational, p. 2.

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

Measure of center
A measure of the typical, middle, or average value for a data set

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

Perihelion
The closest point to the Sun in a planetâ€™s orbit.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Rectangular coordinate system
See Cartesian coordinate system.

Solve by substitution
Method for solving systems of linear equations.

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Vertical component
See Component form of a vector.

Ymax
The yvalue of the top of the viewing window.

Ymin
The yvalue of the bottom of the viewing window.