Unit 8: Differential Equations Assignment 3
1.
2. The growth in the population of China is directly proportional its current population.
a. Set up a differential equation based on this proportionality.
b. Solve this differential equation.
c. In the year 2
Unit 8: Differential Equations - Assignment 1 Solutions
1.
2.
3.
4.
5.
6. Use separation of variables to find the solution to the differential equation subject to the given initial
conditions.
a.
b.
c.
7.
8. Give an example of
a. a differential equation t
Calculus I Homework #2, due Friday, September 23
Please give complete, well written solutions to the following exercises.
1. Suppose g is an even function and let h = f o g. Is h always an even
function? Explain in words why or why not and use simple exam
Calculus I Homework #1, due Friday, September 16
Please give complete, well written solutions to the following exercises.
1. Section 1.1 problem 16
2. Find the domain of the function
f (x) =
1
.
ln(x2 1)
Solution: we need x2 1 > 0 and in addition x2 1 6=
Chapter 3 Assigned problems (6th ed)
3. Consider the following passage from an article in the New York Times (March 9, 2011): In the last few years,
coffee yields have plummeted here [Columbia and in many of Latin Americas other premier coffee regions as
Name: Class: Date: ID: A
Chapter 3 Formula & Theorem Review
Memorize!
1. Make sure to know all derivatives on previous handout with Algebra, Geometry, Trigonometry, and Calculus.
h
2. Denition of the Number e: lim e 1 = 1
h)O h
The above limit is the de
Name: _ Class: _ Date: _
AP Calc AB
ID: A
Chapter 4 Theorems & Formulas
Memorize!
1. Absolute Maximum/Minimum (Extreme Values): The very highest/lowest point on an interval [a, b] at either
endpoints and/or critical points (derivative = 0).
2. The Extreme
Name: _ Class: _ Date: _
ID: A
Differentiation Rules
You Rule!
1.
d
dx
cf (x ) = cf (x )
11.
d
2
[cot x ] = csc x
dx
2.
d
dx
f (x ) g (x ) = f (x ) g (x )
12.
d
[sec x ] = sec x tanx
dx
13.
d
[csc x ] = csc x cotx
dx
14.
d
dx
1
sin x =
d
dx
1
cos
Name: _ Class: _ Date: _
AP Calc AB
ID: A
Chapter 5&6 Theorems & Formulas
Memorize!
1. Left Hand End Points: The area under a curve can be estimated using Left hand end points by forming
rectangles from the left hand side of the function. If the function
Name: _ Class: _ Date: _
ID: A
Formulas and Theorems for AP Calculus
Chapter 2
Memorize and/or KNOW this information for the AP test!
1. Definition of a limit. lim f (x ) = L if and only if lim f (x ) = L and lim f (x ) = L.
xa
xa
xa
+
2. Techniques for f
Calculus Unit 7
Exponents and logs day 1
Lets recall the definition of a logarithm:
If =
=
And the three big rules of logs:
I. log ( ) =
A
II. log b
B
III. log ( ) =
1.
Population around the world grows in very uneven ways. Some countries
have populatio
Unit 8: Differential Equations Assignment 2
1. Newton proposed that the rate at which an object cools is proportional to the difference between the
object and the air around it. For example, if you take a turkey out of the oven and the temperature of
the
Calculus: Unit 6 Assignment 4
1.
2. For 23-26 below, find the general antiderivative.
3. Find the anti-derivative.
a.
x cos( x
2
) dx
b.
c.
d.
4.
x2
3
2x 7
3
dx
5/2
(1
sin(
x
)
cos( x) dx
a.
b.
c.
d.
5. Evaluate the indefinite integrals.
a.
b.
c.
d.
e.
f
Introduction: differential equations means that
equations contain derivatives, eg:
dy/dx = 0.2xy
Ordinary DE: An equation contains only ordinary
derivates of one or more dependent variables of a
single independent variable.
eg: dy/dx + 5y = ex, (dx/dt)
Antiderivatives
Antidifferentiation
The operation of determining the original
function from its derivative is the inverse
operation of differentiation and is called
antidifferentiation.
Antidifferentiation is a process or operation
that reverses different
Integration by Substitution
The chain rule allows us to differentiate a wide variety
of functions, but we are able to find antiderivatives for
only a limited range of functions. We can sometimes
use substitution to rewrite functions in a form that we
can
Calculus Unit 2, Assignment 3
In the following, find
dy
dx
Find the horizontal tangents of the curve.
For 1-4, draw a graph of the requested derivative.
First Derivative
Second Derivative
First Derivative
Second Derivative
First Derivative
Second Derivati
Calculus Unit 4 Assignment 4
You may find these formulas useful: Volume of a cylinder:
Volume of a cone:
V r h
2
SA 2 rh
1
V r 2h
3
Volume of a sphere:
1)
,Lateral Surface Area of a Cone:
4
V r3
3
Farmer Brown is piling his newly harvested corn in a conic
Calculus
Logs and exponentsAssignment 4
Part 1
Calculators are groovy
Show all work and justify all answers.
1.
When Li-An was 15 he had his first job and he earned $1,800/year. As an
18 year old he will earn $2,100/year. Leo has teased him about this
poi
Calculus
Exponential and logarithmic review
Day 2
1.
The Vietnamese living in Taiwan is modeled by the equation = 165 0.26
where t is measured in years from today and P is in thousands of people.
a.
b.
c.
d.
e.
f.
2.
What is the population of Vietnamese i
Calculus Unit 7 Review Worksheet
Part I: Calculators are groovy
1. Scientists observing owl and hawk populations collect the following data. Their initial count for the owl population is
245 owls, and the population grows by 3% per year. They initially ob
Unit 8: Differential Equations Review Worksheet
1.
2.
3.
4.
5. Use separation of variables to find the solution to the differential equation subject to the given initial
conditions.
a.
b.
c.
d. Bonus
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Calculus Unit 7 Assignment 3
Exponents and logs
1.
I give Mare $10,000 and she invests it and recieves a return of 7% per year.
a. Write an equation for this investment as continuous growth.
b. How much will she have in 5 years?
a. How long will it take t