Solutions to Introduction to Analysis
Edward D. Gaughan
March 3, 2013
Notation
Symbol
Ac
f g
N
LHS
RHS
incr.
decr.
cts.
di.
intgbl.
lg(x)
x
an A
lim an
IVT
H
MVT
IFT
Mi
mi
R(x; [a, b])
Meaning
X \ A, where X is the universal set (assumed to be R unless ot
Honors Linear Algebra-Homework 1
Yuanqing Cai
ycai7@jhu.edu
1
1.1 Introduction
2.Find the equations of the lines through the following pairs of points in
space.
(a)(3, 1, 4) and (5, 7, 1)
(b)(2, 4, 0) and (3, 6, 0)
(c)(3, 7, 2) and (3, 7, 8)
(d)(2, 1, 5)
Chapter 3
Continuity
In this chapter we begin by defining the fundamental notion of continuity for real valued
functions of a single real variable. We also introduce the notion of function limit and use this
concept to give equivalent characterizations of
CHAPTER 6
Limits of Functions
1. Basic Denitions
Definition 6.1. Let D R, x0 be a limit point of D and f : D ! R. The
limit of f (x) at x0 is L, if for each " > 0 there is a > 0 such that when x 2 D
with 0 < |x x0 | < , then |f (x) L| < ". When this is th
A
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Introduction
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