AP BC Calc P.2 Properties of Functions
Ferguson Notes
After carefully reviewing the definition of a function, we should have a clearer understanding of what it is, from a rather
practical standpoint, and what it represents. In this second section, we will
AP BC Calc P.2 Properties of Functions
Notes
Ferguson
After carefully reviewing the definition of a function, we should have a clearer understanding of what it is, from
a rather practical standpoint, and what it represents. In this second section, we will
AP BC Calc P.1 Functions & Important Vocabulary
Ferguson Notes
Welcome to the first section of the introductory chapter! In this chapter, we will explore the preliminary skills and
critical thinking that is needed for a calculus class. In all honesty, cal
AP BC Calc P.1 Functions & Important Vocabulary
Ferguson Notes
Welcome to the first section of the introductory chapter! In this chapter, we will explore the preliminary skills
and critical thinking that is needed for a calculus class. In all honesty, cal
Bunch-o-Limits
Find each of the following limits using any method. Show your work! Assume a, b, c, h, and k are constants.
3
3
tan x
x
3
4x 4
1. lim sec
2. lim x 4
3. lim
4. lim
x 7
x 0
x 4
x 0
x
x
6
2x 1 1
x
5. lim
x 0
6. lim
x
sin x 4
4
x
x2 x 6
x 3
Bunch-o-Limits
Find each of the following limits using any method. Show your work! Assume a, b, c, h, and k are constants.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
13.
14.
15.
17.
18.
21.
22.
25.
26.
29. If , then find
23.
12.
16.
19.
20.
24.
27.
28.
30. If , f
Bunch-o-Limits 2 (Advanced)
Find each of the following limits using any (analytical) method. Show your work! Assume a, b, c, h, and k are constants.
1.
2 xx1
lim
x 1
2
9
2 x 1
x 3
2. limsin
x 0
ex 1 x
5. lim
x 0
x2
x 0
2
t 0
1
13. lim
x 0
x
17. lim e
2
Bunch-o-Limits 2 (Advanced)
Find each of the following limits using any (analytical) method. Show your work! Assume a, b, c, h, and k are
constants.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
17.
18.
21.
25.
15.
19.
22.
26.
16.
20.
23.
27.
24.
28.
29.
AP BC Calc 4.5 Approximating Solutions to Non -separable Differential Equations
(Eulers Method/Slope Fields)
Ferguson Notes
Suppose that we were looking at differential equations that were non-separable and could not be solved using a specific
formula. Fo
AP BC Calc 4.5 Approximating Solutions to Non-separable Differential Equations
Ferguson Notes
(Eulers Method/Slope Fields)
Suppose that we were looking at differential equations that were non-separable and could not be solved using a
specific formula. For
AP BC Calc 4.4 Separable Differential Equations
Ferguson Notes
Now that we know what an actual differential equation is, it seems that some of them could be hard to solve. For
instance what if we had a differential equation that was simply a sum of an x a
AP BC Calc 4.4 Separable Differential Equations
Ferguson Notes
Now that we know what an actual differential equation is, it seems that some of them could be hard to solve.
For instance what if we had a differential equation that was simply a sum of an x a
AP BC Calc 4.3 What is a Differential Equation?
Ferguson Notes
Weve somewhat seen differential equations before. When we found a derivative of a function, that was technically a
differential equation. Differential Equations have many practical uses for ex
AP BC Calc 4.3 What is a Differential Equation?
Ferguson Notes
Weve somewhat seen differential equations before. When we found a derivative of a function, that was
technically a differential equation. Differential Equations have many practical uses for ex
AP BC Calc 4.2 Integration By Partial Fractions
Ferguson Notes
In 4.1, we learned how to integrate a lot of different things but we didnt really learn how to integrate advanced
rational functions. That is, its not always true that we can do some substitut
AP BC Calc 4.2 Integration By Partial Fractions
Ferguson Notes
In 4.1, we learned how to integrate a lot of different things but we didnt really learn how to integrate
advanced rational functions. That is, its not always true that we can do some substitut
AP BC Calc 4.1 Basic Antidifferentiation
Ferguson Notes
Antidifferentiation is just what it sounds like: the opposite of differentiation. Its going the other way. What this means
is that imagine that we have a function g ( x) that is the derivative of ano
AP BC Calc 4.1 Basic Antidifferentiation
Ferguson Notes
Antidifferentiation is just what it sounds like: the opposite of differentiation. Its going the other way. What
this means is that imagine that we have a function that is the derivative of another fu
AP BC Calc 4.1 (contd contd) Integration by Parts and Trigonometric Integrals
Ferguson Notes
In the first part of 4.1, the part addressing the method of Integration by Substitution, we found that the Substitution
Rule was a response to differentiation by
AP BC Calc 4.1 (contd contd) Integration by Parts and Trigonometric Integrals
Ferguson Notes
In the first part of 4.1, the part addressing the method of Integration by Substitution, we found that the
Substitution Rule was a response to differentiation by
AP BC Calc 4.1 (contd) Integration by Substitution and Trigonometric Substitution
Ferguson Notes
For integrals that dont have a specific formula that you can just remember, there are a couple of methods that you can
go about using: the first two are somew
AP BC Calc 4.1 (contd) Integration by Substitution and Trigonometric Substitution
Ferguson Notes
For integrals that dont have a specific formula that you can just remember, there are a couple of methods that
you can go about using: the first two are somew
AP BC Calc 4.1 Basic Antidifferentiation
Ferguson Notes
Antidifferentiation is just what it sounds like: the opposite of differentiation. Its going the other way. What this means
is that imagine that we have a function g ( x) that is the derivative of ano
AP BC Calc 3.3 Optimization
Ferguson Notes
The goal of optimization is to find a maximum or minimum value in an application problem. For instance, a CEO of a
company may want to minimize costs while simultaneously maximizing revenues. A surgeon may want t
AP BC Calc 3.3 Optimization
Ferguson Notes
The goal of optimization is to find a maximum or minimum value in an application problem. For instance, a
CEO of a company may want to minimize costs while simultaneously maximizing revenues. A surgeon may
want t
AP BC Calc 2.3 Chain Rule and Inverse Functions
Ferguson Notes
Now that weve seen how to differentiate simple formulas, products, and quotients, we have to learn how to
differentiate composite functions; functions of the form F ( x) f g ( x) .
For instanc
AP BC Calc 2.3 Chain Rule and Inverse Functions
Ferguson Notes
Now that weve seen how to differentiate simple formulas, products, and quotients, we have to learn how to
differentiate composite functions; functions of the form .
For instance, what if we we
AP BC Calc 2.2 The Product and Quotient Rules
Ferguson Notes
Lets review what we can do with functions, from an algebraic standpoint. Let f ( x) and g ( x) be the functions
that were considering. For these two functions, We can:
1) Find the sum:
f ( x) g
AP BC Calc 2.2 The Product and Quotient Rules
Ferguson Notes
Lets review what we can do with functions, from an algebraic standpoint. Let and be the functions that were
considering. For these two functions, We can:
1) Find the sum:
2) Find the difference
AP BC Calc 2.1 The Power Rule and Linearity
Ferguson Notes
During the last couple of sections of chapter 1, we learned about the derivative: its definition, its methodology, and its
applications. Additionally, we covered when the derivative exists and how