Haley, Cochrane,J, Hoa Nguyen, D Valdez, medling, Jason Hole, gatfield, S. Choi, Street,K, Alemansour, mrwalkner, Jacob Tracy, Erbas White, I, Jonathan Luque, Jason nyuin
Solutions: Math 3C, quiz 4
1. Find an equation for the plane that passes through the point (1, 2, 0)
and that contains the line of intersection of the two planes given below:
x+y+z = 2
2x + y + z = 4
Plane 1:
Plane 2:
Note: there are lots of ways to do th
Solutions: Math 3C, quiz 3
1. As shown in the picture below, an object (represented by the large dot)
is lying on an inclined plane. If the object weights 20 lb., find the vector
components of the force of gravity that act parallel and perpendicular to
th
Math 3C, quiz 4
1. Find an equation for the plane that passes through the point (1, 2, 0)
and that contains the line of intersection of the two planes given below:
x+y+z = 2
2x + y + z = 4
Plane 1:
Plane 2:
2. Sketch each surface (described by an equation
Math 3C, quiz 3
1. As shown in the picture below, an object (represented by the large dot)
is lying on an inclined plane. If the object weights 20 lb., find the vector
components of the force of gravity that act parallel and perpendicular to
the ramp. (Yo
Math 3C, quiz 2
1. Prove in painstaking detail that, for vectors u and v in R2 and a scalar b:
u bv = b(v u)
Painstaking detail means that you do not skip or combine steps
and that you provide a reason for each and every step.
Do not use any of the prop
Math 3C, quiz 2
1. Prove in painstaking detail that, for vectors u and v in R2 and a scalar b:
u bv = b(v u)
Painstaking detail means that you do not skip or combine steps
and that you provide a reason for each and every step.
Do not use any of the prop
Solutions: Math 3C, quiz 1
1. Write parametric equations whose graph is the ellipse shown below, drawn
once in a clockwise direction (the orientation is not shown on the graph) as
t varies over the interval [0,1]. [Hint: this problem is similar to the add
Math 251 Notes
Chapter 1
1.2 Exponents, Order of Operations, and Inequality
a n is called an exponential expression where a is called the base and n is called the exponent or power.
Ex 1 Find the value of each exponential expression
a) 4 2
b) 113
3
c)
4
Both (*) where star is a vector equation
and Dag where dag is an augmented matrix
equally represent a system of m-many linear equations in k unknowns
When we take a spancfw_v,vk we take the span of vectors
the set of all linear combinations between vector
Cows, lightning, furniture and yourself. What do all these things have in common? They are
more likely to kill you than a shark. Sharks have a deep-rooted history and have gained significant
respect and admiration from cultures around the globe.
According
1
Chapter 3
Data Description
Section 3.1
Measures of Central Tendency
2
In this section, we will cover three measures of central tendency: mean,
median, and mode.
General Rounding Rule: While performing calculations, do not round until
the final answer is
Chapter 5
Discrete Probability Distributions
Section 5.1
Probability Distributions
1
2
If we flipped a coin twice, the outcomes of the probability experiment would
be S = cfw_HH, HT, TH, TT and we would be interested in a particular outcome
like getting t
Math 10 Practice Exam 2
Before the exam: Study lecture examples and homework as well
On exam day: turn in your homework before taking the exam, bring your calculator
During the exam: you may use a half sheet of notes (half of 8.5 x 11 in. paper, front and
1
Chapter 6
The Normal Distribution
Section 6.1
Normal Distributions
2
In the previous chapter, we covered
discrete probability distributions and, In this section, well cover one
in particular, the binomial probability continuous distribution: the normal
1
Chapter 1
The Nature of Probability and Statistics
Section 1.1
Descriptive and Inferential Statistics
2
3
Data is a fact or proposition used to draw a conclusion or make a decision.
Data describe characteristics of an individual.
A key aspect of data is
1
Chapter 4
Probability and Counting Rules
Section 4.1
Sample Spaces and Probability
2
Probability is a measure of an event occurring.
3
Example
Identifying the Sample Space of a Probability Experiment
Find the sample space for rolling two dice.
4
Solutio
1
Chapter 4
Probability and Counting Rules
Section 4.1
Sample Spaces and Probability
2
Probability is a measure of an event occurring.
3
Example
Identifying the Sample Space of a Probability Experiment
Find the sample space for rolling two dice.
4
Soluti
COMMENTS MADE ON
Math 11 Quiz 2.2 - 2.4
Problem 1 - Find relative extrema; classify as max or min; state x-values; prove max or min; rough
sketch.
Why aren't the points that were calculated put on the graph? 3 times
Practice Factoring. 3 times
Set f' = 0
Math 3a
Exam 3
Spring 2015 10:30 class
Directions:
Show all work and justify all answers.
If you have questions about whether you need to show more work, you may ask.
Use only those techniques of calculus we have covered so far this semester.
Question:
Math 3a
Solutions: Exam 3
Spring 2015 10:30 class
1. (12 points) (a) State the Mean Value Theorem.
If
f(x) is continuous on [a,b] and
f(x) is differentiable on (a,b)
Then: (any one of the statements below is sufficient for your conclusion)
f (b) f ( a)
Math 3a
Exam 2
Spring 2015 9:00 class
Directions:
Show all work and justify all answers.
If you have questions about whether you need to show more work, you may ask.
Use only those techniques of calculus we have covered so far this semester.
Question:
1
Math 3a
Final Exam
Spring 2015 9:00 class
Directions:
Show all work and justify all answers.
If you have questions about whether you need to show more work, you may ask.
Use only those techniques of calculus we have covered so far this semester.
Questio
Math 3a
Solutions: Exam 1
Spring 2015 10:30 class
1. Use the graph of f below to answer the questions that follow.
cs
as
s
d
s
e
b
a point where the derivative is positive.
(a) Put an a on the graph at
Note: there are lots of possible answers. Any place
Math 3a
Final Exam
Spring 2015 10:30 class
Directions:
Show all work and justify all answers.
If you have questions about whether you need to show more work, you may ask.
Use only those techniques of calculus we have covered so far this semester.
Questi
Solutions: Math 3a
Exam 1
Spring 2015 9:00 class
1.
(a) Sketch f ( x ) = 1x .
(b) On the graph from part (a), sketch the tangent line when x = 1.
(c) On the same graph, sketch the secant line between the points whose x-values are
2 and 1.
(d) Which is ste
Math 3a
Exam 1
Spring 2015 9:00 class
Directions:
Show all work and justify all answers. If you have questions about whether you
need to show more work, you may ask.
Question:
1
2
3
4
5
6
7
8
Total
Points:
12
14
12
14
12
12
10
14
100
Score:
Page 1 of 8
M
Math 3a
Solutions: Exam 2
Spring 2015 10:30 class
1. (12 points) Let f ( x ) = sin x. Use the definition of the derivative to find a formula for
f 0 ( x ). You will need to use the fact:
sin( x + h) = sin x cos h + cos x sin h
[Note: you should know the a
Math 3a
Solutions: Exam 2
Spring 2015 9:00 class
1. (12 points) Given the graph of f(x) below, sketch f(x).
A
A
A
6
A
Solution posted separately.
2. (12 points) Evaluate.
d
dx
e
2x
1
4x + 3 ln x cot x + 8
x
1
d 2x
e 4x + 3 ln x cot x x 2 + 8
dx
d
1
1 3
Math 3a
Solutions: Exam 3
Spring 2015 9:00 class
1. (12 points) (a) State the Mean Value Theorem.
If
f(x) is continuous on [a,b] and
f(x) is differentiable on (a,b)
Then: (any one of the statements below is sufficient for your conclusion)
f (b) f ( a)
Math 3a
Exam 3
Spring 2015 9:00 class
Directions:
Show all work and justify all answers.
If you have questions about whether you need to show more work, you may ask.
Use only those techniques of calculus we have covered so far this semester.
Question:
1