Section 1.4 HW
Please give complete, well written solutions to the following exercises.
1. If
lim (f + g ) = 2 and
xa
lim (f g ) = 1
xa
Find
lim f g
xa
2. Find all values of a so that
lim
x 0
ax + 4 2
= 1.
x
3. Compute
|2x 1| |2x + 1|
.
x0
x
Hint: As x 0,
Math for Econ I, Lecture 6-Homework Assignment 9
Due Friday, November 22nd
New York University
Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work,
you will not be given any credit.
Write your
Math for Econ I, Lecture 6-Homework Assignment 1
Due Friday, September 13th
New York University
If you have the textbook, please read chapter 4, especially sections 4.1 through 4.5.
Please write neat solutions for the problems below. Show all your work. I
Math for Econ I, Lecture 6-Homework Assignment 8
Due Friday, November 15th
New York University
Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work,
you will not be given any credit.
Write your
Calculus I
New York University
FINAL EXAM, Spring 2012
Name:
ID:
Read all of the following information before starting the exam:
Show all work, clearly and in order, if you want to get full credit. We reserve the right to
take o points if we cannot see h
Final Review
Exercise 1. Without attempting to evaluate the following indenite integrals, nd the derivative f (x) in each case
if f (x) is equal to
1.
x
1
0 (1+t2 )3
dt
2.
x2
1
x3 (1+t2 )3
dt
Exercise 2. In each case, compute f (2) if f is continuous and
Section 1.1 HW
Please give complete, well written solutions to the following exercises.
1. Sketch the region in the plane that solves the inequality
|x| + |y | 0
Hint: Start by assuming both x and y are positive.
2. Consider the curve that satises the equ
Math for Econ I, Lecture 6-Homework Assignment 3
Due Friday, September 27th
New York University
Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work,
you will not be given any credit.
1. (3 pts)
Transforming graphs and functions; inverses
Jankowski, Math for Econ 1
September 17, 2013
Jankowski, Math for Econ 1
Transforming graphs and functions; inverses
Shifting graphs (5.1)
If we are given a function y = f (x ), then to graph:
1
y = f (x ) + c ,
Math for Econ I, Lecture 6-Homework Assignment 10
Due Friday, December 6th
New York University
Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work,
you will not be given any credit.
Write your
HW 7
Please give complete, well written solutions to the following exercises.
For the problems from the book, please make sure you solve the
right problems by looking up the problem numbers on your EBook
that comes with your web assign. The EBook is the l
HW 6
Please give complete, well written solutions to the following exercises.
For the problems from the book, please make sure you solve the
right problems by looking up the problem numbers on your EBook
that comes with your web assign. The EBook is the l
HW4
Please give complete, well written solutions to the following exercises.
Exercise 0.1. (2.1.30) Find f (a) for f (x) =
4 .
1x
Exercise 0.2. (2.2.46)
(a) If g (x) = x2/3 , show that g (0) does not exist.
(b) If a = 0, nd g (a).
(c) Show that y = x2/3 h
HW5
Please give complete, well written solutions to the following exercises.
Exercise 1. (2.4.48) Find equations of the tangent lines to the curve
y = x1 that are parallel to the line x 2y = 2.
x+1
Exercise 2. (2.5.74) Suppose y = f (x) is a curve that al
Review questions for Midterm exam 1
1. What is the domain of the following function
f (x) =
2. f (x) =
Find
1
tan x
x+
x3 5
, g(x) = 5x 3 and h(x) = ax
f g h,
h g f,
gf h
3. (this IS NOT a multiple choice question) The function f (x) is dierentiable on th
NCRMD
-NCRMD stands for Not Criminally Responsible on Account of
Mental Disorder
-Some Crimes are Planned and are committed in full awareness
of the criminal
-What if the criminal couldnt comprehend the nature of their
action due to mental disorder?
-Send
3: SPECIAL FUNCTIONS
STEVEN HEILMAN
1. Introduction
If you understand exponentials, the key to many of the secrets of the Universe
is in your hand.
Carl Sagan, Billions and Billions
Surprisingly, in spite of the abundant data to the contrary, many people
2: DERIVATIVES
STEVEN HEILMAN
1. Definition of the Derivative
And I, innitesimal being, drunk with the great starry void, likeness, image
of mystery, I felt myself a pure part of the abyss, I wheeled with the stars, my
heart broke loose on the wind.
Pablo
1: INTRODUCTION
STEVEN HEILMAN
1. Applications of Calculus
It seemed a limbo of painless patient consciousness through which souls of
mathematicians might wander, projecting long slender fabrics from plane to
plane of ever rarer and paler twilight, radiat
HW 8
Please give complete, well written solutions to the following exercises.
For the problems from the book (denoted by #), please make sure
you solve the right problems by looking up the problem numbers
on your EBook that comes with your web assign. The
Linearization and dierentials (7.4)
Jankowski, Calculus I
October 22, 2013
Jankowski, Calculus I
Linearization and dierentials (7.4)
Overview and Motivation For Today
Concepts: linearization and dierentials. They help us:
Approximate a functions values
Es
Limits (6.5)
Jankowski, Math for Econ 1
September 18, 2013
Jankowski, Math for Econ 1
Limits (6.5)
In order to understand the concept of a derivative (sections 6.2
through 6.4), we must understand limits.
Jankowski, Math for Econ 1
Limits (6.5)
What is a
Dierenting the inverse (7.3)
Jankowski, Calculus I
October 17, 2013
Jankowski, Calculus I
Dierenting the inverse (7.3)
If f (x ) is a one-to-one function with inverse g (y ), we can
dierentiate g by using f . (without nding a formula for g !)
Theorem (Inv
Sum, product, and quotient rules (6.7)
Jankowski, Calculus I
October 1, 2013
Jankowski, Calculus I
Sum, product, and quotient rules (6.7)
Sum and dierence rule, Example 1
If f and g are dierentiable at a, then
(f g ) (x ) = f (x ) g (x ).
(f + g ) (x ) =
HW 3
Please give complete, well written solutions to the following exercises.
In this section we discussed the tangent line approximation L(x) as the best
rst-order approximation to a given function y = f (x). If we were to construct
L(x) at the point (a,
Section 2.8 Linear Approximations and Dierentials
2010 Kiryl Tsishchanka
Linear Approximations and Dierentials
PROBLEM: Approximate the number
4
1.1.
IDEA: We have seen that a curve lies very close to its tangent
line near the point of tangency. This obse
Section 2.6 Implicit Dierentiation
2010 Kiryl Tsishchanka
Implicit Dierentiation
Some functions can be described by expressing one variable explicitly in terms of another
variable for example,
1x
2
y=x , y=
, y = tan 2x
1 + x3
or, in general, y = f (x). S