HSC 156: Science, Matter, Energy, and Ecology
1. What is matter?
Something that has mass & takes up space
List the 3 forms of matter:
2. What is energy?
It is the capacity to do work
List the 2 forms of energy
3. What is the relation between energy &
2
Functions, Limits and the Derivative
Functions and Their Graphs
The Algebra of Functions
Functions and Mathematical Models
Limits
One-Sided Limits and Continuity
The Derivative
2.1
Functions and Their Graphs
Functions
Function: A function is a ru
1
Preliminaries
Precalculus Review I
Precalculus Review II
The Cartesian Coordinate System
Straight Lines
1.1
Precalculus Review I
The Real Number Line
We can represent real numbers geometrically by points on
a real number, or coordinate, line:
Origi
6
Integration
Antiderivatives and the Rules of Integration
Integration by Substitution
Area and the Definite Integral
The Fundamental Theorem of Calculus
Evaluating Definite Integrals
Area Between Two Curves
Applications of the Definite Integral to
4
Applications of the Derivative
Applications of the First Derivative
Applications of the Second Derivative
Curve Sketching
Optimization I
Optimization II
4.1
Applications of the First Derivative
Increasing and Decreasing Functions
A function f is i
3
Differentiation
Basic Rules of Differentiation
The Product and Quotient Rules
The Chain Rule
Marginal Functions in Economics
Higher Order Derivatives
3.1
Basic Rules of Differentiation
Derivative of a Constant
2. The Power Rule
3. Derivative of a C
5
Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Compound Interest
Differentiation of Exponential Functions
Exponential Functions as Mathematical Models
5.1
Exponential Functions
Exponential Function
The function d
Math 121 Exam 3
Chapter 4
Solve the following problems. Show all steps and justiﬁcations in your responses. You must use calculus
concepts and techniques to solve these problems. Round answers to 4 decimal places if required.
Respond to questions 1 throug
Math 121 Exam 3
Chapter 4
_
Solve the following problems. Show all steps and justifications in your responses. You must use calculus
concepts and techniques to solve these problems. Round answers to 4 decimal places if required.
Respond to questions 1 thr
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6. For the functionf(x,y) =x2 +2xy+2y2 — 6x.+ 12y — l:
(a) Calculate fx(x, y) and fy (x, y). 7! (
£93 I 7! :y g: {2.x 4.465442,
a) (b) Determine all critical points of f, stated as ordered pairs. In the s ace provided here, show evidence
for your response
Riemann Summ problems
Integral
Inventory
Definition of the Derivative
left sum, start left, go right
right sum, start right, go left.
CS=18000
PS=4500
2nd=CS=21333.3
PS=16666.67
Inventory Cost 50
Consumer/Producer Surplus 87,88
Definition of Derivative-15
Slope generating machine=derivatives.
Instantaneous rate of change=what happens at a point. Requires 1 point.
Average rate of change=average rate of change between two points. Requires 2 points.
How do you find the equation of any line- slope, any point o
8
Calculus of Several Variables
Functions of Several Variables
Partial Derivatives
Maxima and Minima of Functions of
Several Variables
The Method of Least Squares
Constrained Maxima and Minima and
the Method of Lagrange Multipliers
Double Integrals