Chapter 4, Section 1 Handout
The Constant Number e: e = lim1 + or e 2.718281828459
Simple Interest, Compound Interest, and Population Growth/Decay Formulas:
If your money is utilizing simple interest, then use A = P (1 + rt ) . If your money is
Chapter 3, Section 3 Handout
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 point is said to be
discontinuous at that point.
Chapter 3, Section 2 Handout
Limits of power functions at infinity: If p is a positive real number and k is any real
= 0 ; xlim kx = ; lim kx = provided that x p is
constant, then lim
a real number for negative values of x. The limits for
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, how
does the length of skid marks change if we increase
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.
The inverse of an exponential function is called a l
Chapter 2, Section 4 Handout
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: all real numbers ( , )
This means the graph is continuo
Chapter 2, Section 5 Handout
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 all real numbers, and the range of f is the set of all p
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 function of
the first variable.
We are now going to look
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 extrema of a function that is
also limited by a second eq
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 integral formulas
and procedures based on the chain rule f
Review for Math 121 Test #1
Using numerical, graphical, and algebraic investigations to find the limits of functions as
x approaches a number lim f ( x) (what is the y-value approaching?).
One-sided and two-sided or
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
f ( x ) dx .
The integrand is f ( x ) , the lower limit of integration is a, and the
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 5.
If f ( c ) f ( x ) for all x in the domain of f, th
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) .
A) Find the domain of f.
B) Find the x and y intercepts
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 AND DECREASING FUNCTIONS:
Graphs of functions generall
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 derivative of
the derivative) can tell us about the shape of a
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.
Economists also talk about marginal revenue and marginal pr