Chapter 4, Section 1 Handout
n
1
The Constant Number e: e = lim1 + or e 2.718281828459
n
n
Simple Interest, Compound Interest, and Population Growth/Decay Formulas:
If your money is utilizing simpl
Chapter 3, Section 3 Handout
CONTINUITY
The idea behind continuous functions is where a graph can be drawn without lifting a pen
off of the paper. A function whose graph is broken at a particular poin
Chapter 3, Section 2 Handout
Limits of power functions at infinity: If p is a positive real number and k is any real
k
p
p
= 0 ; xlim kx = ; lim kx = provided that x p is
p
x
x x
constant, then lim
Chapter 3, Section 1 Handout
In algebra, we solve equations for a particular value of a variable; in calculus, we are
interested in how a change in one variable affects another variable. For example,
Chapter 2, Section 6 Handout
The inverse of the exponential function, which is created by interchanging all x values with their
corresponding y values, is the logarithmic function.
Logarithmic Functio
Chapter 2, Section 4 Handout
Polynomial Functions:
f ( x) = an x n + an1 x n1 + an2 x n2 + . + a1 x + a0
Real number coefficients: a n , a n 1 , a n 2 , ., a1 , a0
Degree of the polynomial: n
Domain:
Chapter 2, Section 5 Handout
Exponential Functions
b > 0, b 1
The equation f ( x ) = b x
defines an exponential function for each different constant b, called the base. The domain of f is
the set of a
Chapter 8, Section 1 Handout
All semester, we have been working with functions with one variable. Even when we
looked at implicit differentiation in Section 4.5, the second variable was considered a f
Chapter 8, Section 4 Handout
We will now consider a particularly powerful method of solving a certain class of maxima-minima
problems. The method of Lagrange multipliers is used to find an absolute ex
Chapter 6, Section 2 Handout
Many of the indefinite integral formulas introduced in the preceding section are based on
corresponding derivative formulas studied earlier. We now consider indefinite int
Review for Math 121 Test #1
Section 3.1
Section 3.2
Section 3.3
Using numerical, graphical, and algebraic investigations to find the limits of functions as
x approaches a number lim f ( x) (what is th
Chapter 6, Section 4 Handout
Definite Integral: See pages 388-389.
Let f be a continuous function on [ a, b] . The definite integral of f from a to b and is
denoted
f ( x ) dx .
b
a
The integrand is
Chapter 5, Section 5 Handout
Finding absolute extrema is one of the most important applications of the derivative. We will be using
much of the material we learned in the first two sections of chapter
Chapter 5, Section 4 Handout
In this section we apply, in a systematic way, all the graphing concepts discussed in the preceding two sections.
GRAPHING STRAEGY FOR
y = f ( x)
Step 1) Analyze f ( x) .
Chapter 5, Section 1 Handout
Since the derivative is associated with the slope of the graph of a function at a
point, it can tell us a great deal about the shape of the graph of a function.
INCREASING
Chapter 5, Section 2 Handout
In the previous section we saw that the derivative can be used to determine when a graph
is rising and falling. Now we want to see what the second derivative (the derivati
Chapter 3, Section 7 Handout
One important use of calculus in business and economics is in marginal analysis. We
introduced the concept of marginal cost earlier. There is no reason to stop there.
Econ