Warm-up Problem
Suppose that the supply curve and demand curve for some product satisfy
qS = 10p 500,
qD = 2500 20p.
(a) Find the equilibrium point.
(b) A tax of $6 per unit is imposed on suppliers. Find the new
equilibrium price.
A few announcements
I
I
Warm-up Problem
Find the domain of the function f (x) =
9 x2
.
x
A few announcements
I
There is no recitation tomorrow.
The first recitation is on Friday, February 3.
A few announcements
I
There is no recitation tomorrow.
The first recitation is on Friday
Welcome to MFE 1!
Do now!
I Pick up handouts by the front entrance
(Syllabus and Calendar)
I Introduce yourself to a neighbor and discuss:
What is Calculus?
How is calculus used in economics?
What do you hope to learn from this course?
Prof. Mutiara Sondj
Warm-up Problem
Let C (q) = q 3 12q 2 + 60q be the total cost for producing q units of a
particular good, where q is in thousands and C (q) is in thousands of
dollars, and 0 q 8.
Find q such that average cost of production is minimized.
A few announcement
CORE-UA.107 Written HW 1
Due: Tuesday, September 20 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although the final answer is important, being able to c
CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 2
Due: Tuesday, September 27 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these problems is clear.
Altho
CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 4
Due: Tuesday, October 11 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Althoug
CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 3
Due: Tuesday, October 4 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although
CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 5
Due: Tuesday, October 25 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Althoug
MATH-UA.211 Written HW5
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although the final answer is important, being able to convey you understand the underlying
concepts is mor
MATH-UA.211 Written HW2
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although the final answer is important, being able to convey you understand the underlying
concepts is mor
MATH-UA.211 Written HW4
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although the final answer is important, being able to convey you understand the underlying
concepts is mor
Math for Economics 1 (Math-UA-211)
Spring 2017
Homework 5
Due: Friday, March 11
at the start of class
Give complete, well-written solutions to the following exercises.
Make sure to write your name and discussion section number, and to staple your solution
Functions, domain/range, and some applications
Supply and Demand, equilibrium,
tax on suppliers/demanders
(4.1-4.5, 5.1 in MFE text; 1.1-1.2 in e-book)
Munn, Math for Econ 1
Munn, Math for Econ 1
Functions, domain/range, and some applications Supply and D
A variety of essential functions
(4.6-4.9 in MFE book, 1.2 in e-book)
Munn, Math for Econ 1
Munn, Math for Econ 1
A variety of essential functions (4.6-4.9 in MFE book, 1.2 in e-bo
Some basic terminology we will discuss:
Revenue, cost, profit
Compound int
Math for Economics 1 (Math-UA-211)
Spring 2017
Homework 4 Solution
Due: Friday, February 24
at the start of class
Give complete, well-written solutions to the following exercises.
Make sure to write your name and discussion section number, and to staple y
Math for Economics 1 (Math-UA-211)
Spring 2017
Homework 2 Solution
Due: Friday, February 10
at the start of class
Give complete, well-written solutions to the following exercises.
Make sure to write your name and discussion section number, and to staple y
Math for Economics 1 (Math-UA-211)
Spring 2017
Homework 1 Solution
Due: Friday, February 3
at the start of recitation
Give complete, well-written solutions to the following exercises.
Make sure to write your name, and discussion section number, and to sta
Math for Economics 1 (Math-UA-211)
Spring 2017
Homework 3 Solution
Due: Friday, February 17
at the start of class
Give complete, well-written solutions to the following exercises.
Make sure to write your name and discussion section number, and to staple y
Name: _
AP Calculus AB - Mr. Robert
List of Derivatives
Powers
d
c=0
dx
d n
x = nx n1
dx
Trigonometric
d
sin(x) = cos(x)
dx
d
cos(x) = sin(x)
dx
d
tan(x) = sec 2 (x)
dx
d
csc(x) = csc(x) cot(x)
dx
d
sec(x) = sec(x) tan(x)
dx
d
cot(x) = csc 2 (x)
dx
Expone
AP Calculus AB - Vivian Robert
Name: _
AP Calculus AB
Worksheet 7.1
Exercise 1 (calculator active) Find the area bounded by the graphs of
f : y = x 2 2x and g : y = 6x x 2
Exercise 2 (no calculator) A parabola has equation y = x 2 4x 1 , and the line
is y
AP Calculus AB - Mr Robert
Name: _
Chapter 7 Notes
Applications of Integration
Section 7.1: Area of a Region Between Two Curves
Objectives Find the area of a region between two curves using integration
Find the area of a region between intersecting curves
AP Calculus AB - Vivian Robert
Name: _
AP Calculus AB
Formative Quiz 5.1: Basic Integration
No calculator allowed
Total points: 16
Exercise: (2 points each) Integrate :
(a)
(3x
(b)
2s
(c)
sin v dv
(d)
(e)
sec
(f)
ax
4
1
+ 4x 5)dx
ds
3
x (x 4)dx
2
7
x
Single Variable Optimization (Chapter 8)
November 1, 2016
Single Variable Optimization (Chapter 8)
Absolute maximum, minimum
Definition
Let f be a function with domain D.
f (c) is the absolute max value of f if f (c) f (x) for all x D.
We call c a maximum
Math for Econ I- Practice Problems
New York University
Derivatives of exponentials and logs and inverse functions.
From the E-Book:
1. Section 3.2: 15, 17, 35, 39
2. Section 3.3: 5, 11, 29, 43, 53, 61, 63,
(The answers to all of these are at the back of t
Math for Econ. I
Class Overview
Trush Majmudar
(Pronounced as troosh - may be one and a half Os)
September 6, 2016
Trush Majmudar (Pronounced as troosh - may be one and a half Os)
Math for Econ. I Class Overview
Office Hours
My office is 719 Warren Weaver
Optimization for functions of multiple variables
(Ch. 13 in MFE textbook; Section 11.7 in e-book)
December 1, 2016
Optimization for functions of multiple variables (Ch. 13 in MFE t
Let f be a function of multiple variables with domain D.
f has a local max
Rates of Change and Derivatives
(6.1-6.4, 6.6 MFE Book, 2.1 E-Book)
September 22, 2016
Rates of Change and Derivatives (6.1-6.4, 6.6 MFE Book, 2.1 E-
Overview
Key concept: f 0 (a), called the derivative of f at a.
What it represents: The instantaneous rat
Limits (6.5 MFE, 1.4 Stewart)
September 13, 2016
Limits (6.5 MFE, 1.4 Stewart)
In order to understand the concept of a derivative (sections 6.2
through 6.4), we must understand limits.
Limits (6.5 MFE, 1.4 Stewart)
What is a Limit?
So far, weve focused ev