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:
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
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
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 derivati
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 valu
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. Th
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
MATH 1P98: Practical Statistics (Spring 2017)
Assignment 1
due Thursday, May 18th (in class)
For our assignments we will be using two different computer programs for each assignment.
Excel is availabl
MATH 1P98: Practical Statistics
(Spring 2017)
Instructor: Andrew Skelton
e-mail: [email protected]
Course Website
All announcements, assignments, solutions, lecture notes and grades will be posted on
1p92 Sample final exam questions
1. The diagram below shows the AE line for the economy.
AE
AE=Y
AE1
Real GDP
a) Label the autonomous expenditure A in the diagram.
b) Label the equilibrium level of GD
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
f