 4.2.1: Apply Theorem 4.2.4 to determine the following limits: (a) lim (x +...
 4.2.2: Determine the following limits and state which theorems are used in...
 4.2.3: F. d lim JI + 2x  J1 + 3x h 0 . 1n 2 w ere x > . x0 X +2x (b) lim...
 4.2.4: Prove that lim cos(1/x) does not exist but that lim x cos(l/x) = 0....
 4.2.5: Let 1, g be defined on A ~ R toR, and let c be a cluster point of A...
 4.2.6: Use the definition of the limit to prove the first assertion in The...
 4.2.7: Use the sequential formulation of the limit to prove Theorem 4.2.4(b).
 4.2.8: Let n eN be such that n ~ 3. Derive the inequality x2 !:: x 11 !::...
 4.2.9: Let f, g be defined on A to 1R and let c be a cluster point of A. (...
 4.2.10: Give examples of functions f and g such that f and g do not have li...
 4.2.11: Determine whether the following limits exist in JR. (a) lim sin(ljx...
 4.2.12: Let/: 1R+ 1R be such that f(x + y) = f(x) + /(y) for all x, yin R....
 4.2.13: Let A ~ 1R, let f: A + 1R and let c e 1R be a cluster point of A. ...
 4.2.14: Let A ~ 1R, let f : A + R, and let c e R be a cluster point of A. ...
Solutions for Chapter 4.2: 4.2 Limit Theorems
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 4.2: 4.2 Limit Theorems
Get Full SolutionsThis textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Chapter 4.2: 4.2 Limit Theorems includes 14 full stepbystep solutions. 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. Since 14 problems in chapter 4.2: 4.2 Limit Theorems have been answered, more than 6851 students have viewed full stepbystep solutions from this chapter.

Amplitude
See Sinusoid.

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Complex fraction
See Compound fraction.

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Cosine
The function y = cos x

Descriptive statistics
The gathering and processing of numerical information

Directed angle
See Polar coordinates.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Implied domain
The domain of a function’s algebraic expression.

Magnitude of a real number
See Absolute value of a real number

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Parallel lines
Two lines that are both vertical or have equal slopes.

PH
The measure of acidity

Quartic function
A degree 4 polynomial function.

Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

Supply curve
p = ƒ(x), where x represents production and p represents price

Tangent
The function y = tan x

Unit circle
A circle with radius 1 centered at the origin.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.