More Examples for Conic Sections
Math 141 sections 4 and 5
1. For the following parabola, identify the focus, directrix and sketch its
(y + 1) 2 = "4(x " 2)
graph.
2. For each of the following, decide
Section 1.6 Inverse Functions and Logarithmic Functions
Math 141
Objective 1- A function is one-to-one if each domain variable maps to just
one range variable AND each range variable comes from only o
Lecture Outline for Section 2.6 and section 2.7
Derivatives and Rates of Change; The Derivative as a function
Math 141
Extra Problems from text to work: 2.6 # 5,7,11,13,16,17,27, 30,43a and b
2.7 # 1,
Lecture Math 141
Section 2.4 Continuity
Extra h/w to try in the text:
#3,13,15,1727,29,31,33,35,40,41,43
I.
Definition: A function is continuous at x = a if lim f (x) = f (a) .
x !a
Note this implies
Class Notes Outline for Appendix B Coordinate Geometry
Found in back of the book starting on page A7
Topics
I.
Lines
II.
Circles
III. Parabolas
IV. Ellipses
V.
Hyperbolas
I.
Lines
Slope
Parallel
Perpe
Section 2.3 Calculating Limits using the Laws of limits
Limit Laws are written in the text.
#1 - #11
Make sure you know these and can these in practice.
Examples for class:
a) Given the following info
Combustion, Explosion, and Shock Waves, Vol. 32, No. 5, 1996
GENERAL
MATHEMATICAL
MODEL
FOR FOREST FIRES AND ITS APPLICATIONS
A. M. Grishin
UDC 533.6.011.6
A review is presented of the results of phys
Lecture 3.3 Derivatives of Trigonometric Functions
Optional problems from the text: #1-13 odd, 15,16,19,21,29,31,35,37
To prove the derivatives of y = sin " and y = cos" well need to results
of two li
Math 141
Fall 2012
Instructor: Elizabeth J. Dempster
Office :
SAS 3240
Office Hours: MWF 11:15-12:10 and by appointment
Thursday elluminate office hours tba
Email:
[email protected]
Communication Poli
Math 141
Fall 2012
Instructor: Elizabeth J. Dempster
Office :
SAS 3240
Office Hours: MWF 11:15-12:10 and by appointment
Thursday elluminate office hours tba
Email:
[email protected]
Communication Poli
Lecture 3.2 The Product and Quotient Rules
Optional extra problems in the text p. 188# 1-31 odd, 33, 41, 43, 47, 51
I.
Product Rule: p. 194 in text
d
df
dg
( f " g) =
" g(x) +
" f (x)
dx
dx
dx
= f " #
Section 3.4 Chain Rule
Optional Homework from the text:
3.4 #1-45 every other odd, 41,43,45,47,51,53,61,65,73
Chain Rule:
Page 198, the rule is written out in the red box,
F = f og
F "(x) = f "(g(x) g
Section 3.5 Implicit Differentiation
Sometimes y is not written as an explicit function of x but y is an implied function of x.
Consider the equation of the circle x 2 + y 2 = 16
What implied function
Notes for section 3.7 and 3.6
Lecture 3.7 Derivatives of Logarithmic Functions
3.7
I. Derivatives of Logarithmic Functions
II. Method of differentiation logarithmic differentiation
Optional list of pr
MODULE 5: FUNCTION TRANSFORMATIONS
MEGAN SAWYER
SEPTEMBER 1, 2010
The following table is a summary of the rules for transforming functions. (Table courtesy
of Matthew Comer, NCSU.)
Equation
Vertical
S
Q1
Month
Eletric Bills
May
June
180.21
July
Aug
Sept
Oct
Nov
192.26
223.32
254.14
217.8
198.31
165.78
Eletric Bills
300
250
200
150
100
50
0
0
Q2
Month
Sales
2
4
Jan
6
Feb
10
March
17
8
April
29
10
Ma
Elluminate: Assignment 1
Elluminate is the program we use to set up and hold problem sessions in a
virtual classroom. On Tuesdays, you will attend these problem sessions by
logging into the virtual sp
.
.
.
.
.i
.,. m. .
MA141 - Fall 2015 Test 1 Form A
READ and follow directions carefully. You may NOT use a aphing calculator or a communication
device of any type during the test. You may use a
MA 141 Chapter 2
Section 2.7: Related Rates
We do not deal with multivariable calculus in this course, but we can deal with two
functions u = f (t) and v = g(t) that each depend on a common variable t
MA 141 Chapter 2
Section 2.1: The Derivative of a Function
Last class, we found the formula for instantaneous velocity, which was essentially the same
as the formula for slope of a tangent line that w
NCSU MA 141 Fall 2016
Test #1 Form B
September 9
Please write your full name and Test Form (A or B) on the front of the blue book provided
and put all answers and work within. Write your row on the fr
MA 141 Chapter 0
Section 0.1: Real and Complex Number Systems
Sets:
Def: A set is a collection of objects. If x is an object in a set S, we say x
is an element of S and we write x S.
If every element
MA 141 Chapter 2
Section 2.5: The Chain Rule
Example: Find the derivative of h(x) = sec(5x) + (x3 + 4x + 1)6 .
We do the derivative of the "outside" function first - sec(u).
Example: Find the derivati
arranging two coordinate lines at right angles, with the
on those lines to the right and up as shown in Figure
axis is called the x-axis and the vertical axis is called t
The utility of this arrangeme
MA 141 Chapter 1
Section 1.3: Continuity
CHAPTER 1. THE LIMIT
We now have the tools to formally define a continuous function.
However this
does not persist fo
have the plot of a f
defined by
Def: A fu
MA 141 Chapter 1
Section 1.1: Introduction
In general, we like to work with "nice" functions. We are building tools to properly define
continuous functions.
Non-rigorously, what is a continuous functi
MA 141 Chapter 2
Section 2.2: Basic Dierentiation Rules and
Section 2.3: Power Rule and Rational Functions
We want to build general rules to make dierentiation faster.
Example: Use the limit definitio