Chapter 1
Intervals
Open Interval: The set of all real numbers that lie strictly between two fixed
numbers a and b is called an open interval (a,b). It consists of all real numbers x that
satisfy the inequalities a<x<b. and it is called open because neith
Chapter 4.2 Intervals of Concavity
First Derivative f: Is the slope the first derivative tells us how whether a
function is increasing or decreasing, and by how much it is increasing or
decreasing. This information is reflected in the graph of a function
Chapter 2
Functions
Function: A rule that assigns to each element in a set A one and only one element in a set B.
The set A is called the domain of the function.
Y=f(x) as x takes on all possible values in its domain, is called the range.
- Domain is a se
Chapter 6.1
Antiderivatives and Rules of Integration
A function f is an antiderivative of f on an interval I if F(x) =f(x) for all x in I
An antiderivative of function f is a function F whose derivative is f.
For example, F(x)=x2 is antiderivative of f(x)
Trapezoidal Rule
CHAPTER 7.3
- We assume that
to simplify the derivation of the
Trapezoidal Rule
- The result is valid without this restriction
- Begin by dividing the interval [a,b] into subintervals of equal length
- By means of the (n+1) points x-0= a
Chapter 5.5
The derivative of ln x
d
1
ln| x| (x 0)
dx
x
To derive the rule, suppose x>0 and write f(x)=ln x in the equivalent form x=ef(x)
Differentiating both sides of the equation with respect to x, we find using the chain
rule
1=ef(x)*f (x)
From which
Chapter 3
Differentiation
Rule 1: Derivative of a Constant
d
(c) 0
dx
The derivative of a constant function is equal to zero
- The graph of a constant function is a line parallel to the x axis
Rule 2: The Power Rule
d
If n is any real number, then (xn ) n
Chapter 8
8.1-Functions of Several Variables
Functions of Two Variables
A real-valued function of two variables consists of
1. A set A of ordered pairs of real numbers (x,y) called the domain of the
function.
2. A rule that associates with each ordered pa