> f:=x->(x-1)/(x^2+x-2);
(1)
> limit(f(x),x=1);
1
3
(2)
> Limit(f(x),x=1,left);
(3)
> Limit(f(x),x=1,left)=limit(f(x),x=1,left);
(4)
> Limit(f(x),x=1,right)=limit(f(x),x=1,right);
(5)
> plot(f(x),x=-5.5);
10
8
6
4
2
0
2
4
x
>
Spreadsheet(1)
A
B
C
D
E
F
G
f(x) = x2 + 8,
(1, 9)
(a) Find an equation of the tangent line to the graph of f at the given
point.
Using the derivative rule you dnt
need to use the formula
f(x)=2x+0=2x
f ( x x)f (x )
x
2
+8
( x x)
2
(x + 8)
x 22 x x( x 2 +8x 28)
x
2
x
2 x x
(2 x x)=
Find an equation of the line that is tangent to the graph of f and
parallel to the given line.
Function
Line
f(x) = 2x2
6x y + 4 = 0
f(x)=4x(just use the derivative rule, dnt need all of that.)
6x-y+4=0
-6x -4
_
y=6x+4-> m=6
f ( x x)f (x )
x
x x 2(2 x 2 )
Quiz One (9/30/14) MAT 150
Prof. He Name '
The table on the right shows the heights, in inches, of Namg
one possible starting lineup Knicks players during the Pablo Prigioni
20132014 regular season. Answer the following
questions. (Note: If an answer is n
Chapter 6
Normal Probability Distributions
Statistical Literacy and Critical Thinking
1. Normal Distribution When we refer to a normal distribution, does the word normal
have the same meaning as in ordinary language, or does it have a special meaning
The Empirical Rule and Chebyshevs Theorem
The learning objectives are:
1.
To learn what the value of the standard deviation of a data set implies about how the data scatter away from the mean as
described by the Empirical Rule and Chebyshevs Theorem.
2.
T
If you have Excel 2010 or 2007:
Step 1:
Open a blank spreadsheet in Excel. Enter the data set in a
blank Excel spreadsheet including x and y as the column
headings. (Here, lets use the numbers of hours spent on
studying vs. the grades received on an exam
Reference Sheet Notations and Formulas
Population
Size
N
Mean
=
=
x
N
(x)2
Sampling Distribution
N x
x
x =
xf
f
x =
n
( x x )2
x =
n1
x
N x
or
2
N ( x )( x )
2
N2
x =
or
s=
x f
f
N x
or
2
n ( x )( x )
2
n(n1)
(where
(x x)2
x =
N x ( x2 ) ( x )
2
N
Quiz 9
Prof. He
MAT 150
Name _
1. From a sample of 16 female college students, their mean height is 63.5 inches. If the heights of all females
are normally distributed with standard deviation of 2.6 inches, construct a 99% confidence interval for the
mean
Homework Collection
MAT 150
Throughout the semester there will be a total of 18 homework assignments. Since there are a large
number of students in the class, I will not collect single homework of yours. I will only collect 6
homework assignments from eac
Handout 1 (2/2/15)
MAT 150
Given below are recent measurements from the Old Faithful geyser in Yellowstone National Park. The time
intervals between eruptions are matched with the corresponding times of duration of the geyser; thus the
interval of 76 min
Spring 2015
MAT 150
Final Review
You are allowed to use a calculator, however, you still have to show work and it has to be an actual calculator and it
cant be a calculator from your cellphone. There will be show-work problems as well as multiple-choice p
Using Excel 2013 to Make Charts
A. Bar charts with gaps
A bar chart in Excel is actually a horizontal bar chart. A vertical bar chart in Excel is
The following is the general procedure to make a column chart in Excel, i.e., a
(vertical) bar chart in most
I met with Byron at his residence. I notified Byron that I cleaned while he was outing of town in PA, to
explain Byron to ensure that he needs to comply with house rules, is to keep the apartment clean every
day. Byron understood it and he will clean the
Takenya Tucker
884 Ashford St, Brooklyn
N.Y.1120
Phone: 347-499- 2852
Takenyatucker@yahoo.co
m
EXPERIENCE
Hale & Hearty , New York,NY Team Lead
September 2010 - PRESENT
Effectively lead the restaurant while the Manager or Asst. Manager is
not present.Resp
APEX
C
Version 3.0
Gregory Hartman, Ph.D.
Department of Applied Mathema cs
Virginia Military Ins tute
Contribu ng Authors
Troy Siemers, Ph.D.
Department of Applied Mathema cs
Virginia Military Ins tute
Brian Heinold, Ph.D.
Department of Mathema cs and Com
Math Notes
Derivatives of Common Functions Theorem
Chapter 3.1 - Extreme Values
Consider Figure 3.1. The function displayed in (a) has a maximum, but no
minimum, as the interval over which the function is defined is open. In (b), the
funcon has a minimum,
Chapter 8
Trigonometry (Greek word) means measurement of triangles. An angle is
formed by rotating a ray about its endpoint (vertex) starting with the initial side and
ending at its terminal side.
Positive angles are generated by counter clockwise rotatio
7.1 Exponential Functions
x
A function of the form f (x) = b where b > 0 and b !1 is called an
exponential function of base b. The independent variable x represents
any real number.
x
Ex. f (x) = 5 where base = 5
! 2$
" 3%
x
Find the value of each listed
MAT301-111 Practice Exam #2
1)
Find the differential dy of the given function
f (x) = x 1 x 3
2)
Find the derivative given that f (x) = x (x 4)
3)
Find
4)
A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder
slides away fro the