Math 260 - Week 3 Lab Name: AWN m 09 $40 6,541 .
ln calcuius, much effort is devoted to determining the behavior of the graph of a function over an
interval on the Cartesian Plane. '
Finding x & y intercepts, asymptotes, intervals of increasing or decrea
MATHZSOWeek 4 Lab Name: 5 Avmg n54 5ko @394
Part i: The Trig Derivatives
Atthough the derivative of each tn'g function can be found by using trig identities and the formula
limbo W , it is far simpler to memorize them because they will be used in many of
Math 260 - Week 2 Lab Name: Aim/W440 39! avg,
As we have seen, using limheo w to nd a derivative each time is a long process and often
cumbersome. But, there are a few algorithms that work perfectly for nding derivatives. They are the
power rule, the prod
6.1 Estimating with Finite Sums
LRAM is left corner touches the curve
RRAM is right corner touches the curve
MRAM is the midpoint touches the curve
x ( f ( x 1 ) + f ( x 2 ) + f ( x n) )
If you are unable to factor out x, then you must multiply each
5.1: Extreme Values of Functions
Graph can have absolute max/min and local max/min
Derivative graph shows max/min when x=0
Finding extreme values: f ' ( c )=0 then sign chase
Plug in nearby values to derivative to find out signs
Maximum if sign chang
AP CALCULUS EXAM REVIEW
Asymptotes
Horizontal
Vertical
y = ratio of coefficients
if the highest
exponents of the top and bottom are the same
y=0
if the bottom exponent is larger
none if the bottom exponent is smaller
To find vertical asymptotes set denomi
1. Explain why trigonometric functions are periodic.
There are many cases in which more than one angle has the same value for its sine, cosine, or
some other trigonometric function. This phenomenon exists because all trigonometric functions
are periodic.
Chapter 9 section 9.1
In Exercises 5 to 24, solve each system of equations by
using the substitution method.
x5
cfw_ y=3
y=5 x7
#15:
In Exercises 25 to 42, solve each system of equations by
using the elimination method.
#31:
cfw_63xx+2y=4
y=8
#37:
cfw_
3
Chapter 4
Section 4.1
1
7
1
#21: f ( x )=2 x+ 7 ; f ( x ) = x
2
2
1
1
f ( f ( x ) ) =xf ( f ( x ) ) =x
1
7
f ( f 1 ( x ) ) =2 x +7=x7+7=x
2
2
1
7
7 7
f 1 ( f ( x ) )= ( 2 x+ 7 ) =x + =x
2
2
2 2
1
f ( x )f ( x ) are inverse of one another
(
)
1
1
#23: f
1. What is the geometric sense of a linear system in two variables and a linear system in
three variables?
For a system involving two variables (x and y), each linear equation determines a line on the xyplane. Because a solution to a linear system must sa
1. What is a composition of functions? What is the difference between the composition
and the product of two functions?
Composition of two function
let f ( x) and g( x) are two function
composition of function is f of
Example: f ( x )=x 2 +2; g ( x )=x +
1a. Compare methods of solving linear equations and methods of solving linear inequalities. What
do they have in common? What is different?
The methods of solving both the linear equalities and inequalities are almost similar, the only difference is
that
Z-Score
From area to z
From z to area
-1.6449
0.9772
Area
z-score
t-score
From t to area
From area to t
0.05694
2.86093
t-score
Alpha
0.05
2
2
0.01
n
n
25
20
tails
2
Finding Z value
Know X, Finding Z
X
Std Dev
Mean
Z
8
1.5
6.29
1.14
Know Z, Finding X
Z
St
Step 2 for hypothesis testing
Critical Values
Critical values for z
Apha
One tail test
Two tail test
0.05
-1.6449
-1.9600
Formulas
=normsinv(alpha)
Critical values for t
Apha
n
One tail test
Two tail test
0.05
5
2.1318
2.7764
=tinv(alpha, deg_freedom)
Ste
Function
Excel
Formula
From t to area
From area to t
p-value for t score
From z to area
From area to z
p-value for z score
Area between mean and x
=tdist(x,deg_freedom,tails)
=tinv(probability, deg_freedom)
=tdist(x,deg_freedom,1)
=normsdist(z)
=normsinv(
Statistics Lab #6
Name:_Sihan Wang _D01599667_
Statistical Concepts:
Data Simulation
Discrete Probability Distribution
Confidence Intervals
Calculations for a set of variables
Open the class survey results that were entered into the Excel worksheet.
Statistics Lab Week 2
Name:_Sihan Wang _D01599667_
Math221
Statistical Concepts:
Using MINITAB
Graphics
Shapes of Distributions
Descriptive Statistics
Empirical Rule
Data in MINITAB
MINITAB is a powerful, yet user-friendly, data analysis software pa
Statistics Lab Week 4
Name:_Sihan Wang _D01599667_
MATH221
Statistical Concepts:
Probability
Binomial Probability Distribution
Calculating Binomial Probabilities
Open a new MINITAB worksheet.
We are interested in a binomial experiment with 10 trials.
1. In the standard normal distribution the means is always(Points:3)
0 -OUR ANSWER
1
2
none of these
2.The area under a normal curve with mu = 15 and sigma = 2 is(Points:3)
0
1 -OUR ANSWER
2
none of these
3.If Larry gets a 70 on a physics test where the m
Math 221 Statistics Lab Week 2
Name: Kaixuan Chen
Statistical Concepts:
Using MINITAB
Graphics
Shapes of Distributions
Descriptive Statistics
Empirical Rule
Code Sheet for Data in Excel
Variable
Question
Name
Drive
Question 1 How long does it take yo
Confidence Internval for z (n30)
Note: Yellow cells are input
Note: Green cells are answers
Mean
s
n
Confidence level
Error
1553.40
0.25
37
90%
0.07
Lower Limit
1553.33
Formulas used
E (error) = z * s / sqrt (n)
Confidence interval = mean + and - (error)
Drive
36
State
MI
80 NV
76 PA
88 CA
54 FL
6 OR
4 NY
55 OH
36 TX
71 MI
25 GA
28 NY
73 FL
63 PA
78 CA
94 KY
36 OR
25 CA
76 NY
80 CA
blue
white
silver
black
green
silver
blue
dark blue
orange
blue
silver
black
green
silver
blue
red
blue
silver
red
Temp
51
Ra
Fiber Type
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
High Fiber
Me
Statistics Lab Week 2
Name: Jun Xi Zhou_
Math221
Statistical Concepts:
Using MINITAB
Graphics
Shapes of Distributions
Descriptive Statistics
Empirical Rule
Data in MINITAB
MINITAB is a powerful, yet user-friendly, data analysis software package. You
Statistics Lab #6
Name:_Jun Xi Zhou_
Statistical Concepts:
Data Simulation
Discrete Probability Distribution
Confidence Intervals
Calculations for a set of variables
Open the class survey results that were entered into the MINITAB worksheet.
We want