Notes to Chapter 1
Working with growth rates
Let y0 be the initial value of variable y, and suppose that the variable is growing at a constant rate
of g. The future value of y will be:
After 1 year:
y1 = y 0 (1 + g ) .
After 2 years: y 2 = y1 (1 + g ) = y
Principles of Economics:
1) People make trade-offs
Allocating time to priority until you run out
2) Opportunity Cost: cost of something is what you give up to get it
Explicit cost = regular cost
Ex. Going to a movie:
o Explicit Costs
2.1: The Tangent and Velocity Problems
Math 111 - 2.1 - Professor Louie
A tangent line to the function f (x) at the point x = a is a line that touches the graph of f at x = a
and is parallel to the graph at that point.
*If the function is not a straight l
2.6: Limits at Infinity, Horizontal Asymptotes
Math 111 - 2.6 - Professor Louie
We have been working on how to find a limit as x approaches some specific value. But what if we
wanted to look at the limit as x generally gets really small or really large?
1.5-1.6: Exponential & Logarithmic Functions
Math 111 - 1.5-1.6 - Prof. Louie
General Exponential Functions
The general exponential function with base a is defined by
f (x) = ax
where ax = ex ln a .
Law of Exponents:
For real numbers x, y, and a, b > 0:
2.3; 2.5: Calculating Limits Using Limit Laws; Continuity
We now introduce more methods on how to calculate limits.
If c, n are constants where n > 0, then:
lim c = c
lim x = a
lim xn = an
Ex: Evaluate the following limits: