6CO2 + 6H20 +
light energy ->
C6H12O6 + 6O2
Abiotic
Chemical Equation for Photosynthesis
Absorption
Drinking Water Treatment Process
Using an absorptive surface, like charcoal, can remove additional o
Chapter 12
Sustaining Aquatic Biodiversity
Its A Small World After All
Outline
Aquatic Biodiversity
We know very little about the earths aquatic biodiversity because there has been so little explorati
Chapter 4
Evolution and Biodiversity
Its A Small World After All
Outline
Origins of Life
A. Chemical evolution of organic molecules, biopolymers, and systems of chemical reactions were
needed to form
Chapter 8
Population Ecology
Its A Small World After All
Outline
Population Dynamics and Carrying Capacity
A. Populations change in size, density, and age distribution, most members of populations liv
HUMANS AND SUSTAINABILITY: AN OVERVIEW
Chapter 1
Environmental Problems, Their Causes, and Sustainability
Its A Small World After All
Outline
Living more sustainably
A. Environmental science studies h
ECOLOGY AND SUSTAINABILITY
Chapter 2
Science, Systems, Matter, and Energy
Its A Small World After All
Outline
The Nature of Science
A. Science assumes that events in the natural world follow orderly p
Chapter 24
Economics, Environment, and Sustainability
Its A Small World After All
Outline
Economic Systems and Sustainability
A. An economic system produces and distributes goods and services by using
Chapter 6
Aquatic Biodiversity
Its A Small World After All
Outline
Aquatic Environments
A. Saltwater and freshwater aquatic zones cover about 71% of the earths surface. These are the
equivalent of ter
Chapter 7
Community Ecology
Its A Small World After All
Outline
Community Structure and Species Diversity
A. Ecologists use three characteristics to describe a biological community:
1. Physical appear
Multiplying Fractions and Mixed Numbers
When we ask, "What is 4/5 of 55?" or "What is 1/6 of 18/5?", we are really
asking, "What is 4/5 times 55?" and "What is 1/6 times 18/5?". When dealing with
frac
Least Common Denominator (LCD)
A common denominator of two numbers is a number that can be divided by the
denominators of both numbers. For example, 1/6 and 4/9 have common
denominators of 18, 36, 54,
Fractions
A fraction describes a part of a whole. The number on the bottom of the fraction
is called the denominator, and it denotes how many equal parts the whole is
divided into. The number on the t
Expressing Fractions as Decimals
Sometimes we will want to work with decimals instead of fractions. To convert
fractions to decimals, simply divide the numerator by the denominator, either
using a cal
Expressing Decimals as Fractions in Lowest Terms
Sometimes it is easier to work with fractions than to work with decimals. It is
therefore important to learn how to change decimals into fractions. The
Adding and Subtracting Fractions
We can only add or subtract fractions when they have the same denominator.
Therefore, the first step in adding or subtracting fractions is writing them as
fractions wi
Equivalent Fractions
Two fractions are equivalent if they express the same part of a whole. For
example, 2/3 and 4/6 express the same part of a whole. 12/9 and 4/3 are also
equivalent.
Two fractions a
AP Calculus: Limits
Names_
A. Sketch a graph that meets the following criteria:
1.
2.
lim f (x) 2
lim f (x) 4
x2
3.
lim f (x) 2
x4
4.
lim f (x) 1
x
x1
lim f (x) 4
x1
5.
lim f (x) 3
x2
lim f (x) 2
x2
f
AP Calculus AB
Chapter 3
1.
Name_
2.
3(x h)2 3x2
lim
h0
h
3.
f (x)
7 x h 2 x h 7x 2x
4
lim
5.
h
4
6.
2
11 x h 3 x h 4 11x 3x 4
3
lim
h
d
11x4 7x3 8x2
dx
8.
3
h0
9x4 9a4
xa
x a
lim
y x 8x 5x 3x 4
dy
Chapter 2 Review
1. lim ( x x 1)
x
2. f ( x) 2
x 16
x3 2 x
3. lim 2
x 3 x 5
x2 4
4. f ( x)
x2
3
2
x 2
5. lim(e x x)
x
(find VA, HA and holes)
(find VA, HA and Holes)
x 3 9 x 14
x
2 x 3
6. lim
6. f
Calculus Chapter 2 Limits (Day 3)
HOMEWORK
Name_
Find the (a) lim f ( x), (b) lim f ( x), and (c) all asymptotes (horizontal and vertical) and holes in the
x
graphs.
1.
f ( x)
2. f ( x)
3.
4
x 1
x
LHpitals Rule
Indeterminate Forms 0,-, 00, 1,0
Examples:
1.
=
2 x
lim x e
x
2.
1
lim x sin
x
x
3.
=
1
1
ln x x 1
lim
x 1
4.
1
lim 1
x
x
5.
lim x x
x 0
x
=
=
Homework:
1.
=
1 1
lim
x 0 x
x
2.
AP Calculus
Chapter 2
1.
a.
b.
c.
d.
e.
Name_Pd_
Given f(x) = x3 5x2.
Find the average rate of change over [-2, 5]
Find the instantaneous rate of change at x = 5
Give the slope of the curve at x = -1
AP Calculus
Name_
Given the graph of f(x), graph f (x).
1.
2.
y
y
x
x
AP Calculus
Given the graph of f(x), graph f (x).
Name_
1.
2.
y
y
x
x
Given the graph of f (x), graph f(x)
3. f(1)=2
4. f(-3)= 1
y
Advanced Calculus
Improper Integrals Quiz Review
Using the direct comparison or limit comparison test, determine if the following
integrals diverge or converge.
1.
2.
1
ln x
1 cos 2 x
dx
x
3 dx
x
e
Advanced Calculus
Name_
Improper Integrals
Evaluate the following integrals or state that it diverges. If you use the direct
comparison test or the limit comparison test to determine the integral dive
Limit Review
Limit
x 2 16
lim
x 4 x 4
2 x3
lim
x x 5
lim x3 2 x 2 1
x 2
2 x2 3
x 5 x 2 7
lim
ex
x x 3
lim
lim
x 0
7x
x 5
5x2
lim 2
x 2 x 4
lim
x 0
ln x
x
2 x 3, x 0
lim
x 0
2
x 3, x 0
x2
lim 2
x 1
LHpitals Rule
The Indeterminate Forms 0/0 and
LHpitals Rule: If f(a)=g(a)=0, f and g are differentiable on an open interval I containing a, and
f ( x)
f ( x)
f (a )
lim
or
that g(x) 0 on I if x a, t
4670 - 1 - Page 1
AP CALCULUS
EXACT VALUES TRIG REVIEW
Name _
_ 1)
Find the exact value of sin
.
_ 8)
Find the exact value of tan
.
_ 2)
Find the exact value of sin
.
_ 9)
Find the exact value of tan
Calculus I
Worksheet #8
Review for Test 2 Limits and Continuity
1
sin5x
lim
x 0 cos4 x
2
sin2 3x
lim 2
x 0 x cos x
3
sin5x
lim 1
x 0
sin x
3
4
x
lim
x 0 tan x
5
lim
x
1 + sin x
1 cos x