EXPLAINING ADDITIVE AND MULTIPLICATIVE
INVERSES
JORDAN DUBUQUE
ADDITIVE INVERSE PROPERTY:
The additive inverse of a number is the same number with the opposite sign. When adding
a number to its additive inverse, the sum will always be 0. This is the addi
Assignment: Distributive Property Problem Set
Write an equation to solve each problem. Apply the distributive property and show all the steps
needed to find the solution. Think about whole numbers to use to solve each problem. Write a
sentence that tells
HISTORY OF LIFE
LAB
Jordan Dubuque
October 4, 2016
When and where did
cyanobacteria life begin and how
do
we
know
this?
The oldest evidence of life belongs to microscopic marine
organisms during the Precambrian era (roughly 3.5 million years
old).
Fossil
Jordan Dubuque
Journal: Cancer Cells
There are more than 200 different types of cancer. 1 in 2 people in the UK will get cancer in their
lifetime. Cancer starts when gene changes make one cell or a few cells begin to grow and multiply too
much. This may c
Assignment: Analyzing Decimals, Fractions, and Percents
Choose three problems to solve. Show all your work, including how you found your answer. Write
a description of how you found each answer and be sure to write an answer to the question.
Then use stat
First-Half of the Semester
Understand the relationships between
Paradigm- framework observation that shapes what we see and how we
understand it.
-ARENT T/F but useful or less useful.
-different lens how we can see the world.
Theory- relevant to why quest
MTH 245 Calculus I
Midterm I Fall 2007 Form A
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Select the correct answer.
1. Determine whether the function f (x) = x2 + x is even, odd, or neither.
(a) even
(b) odd
(c) neither even nor odd #
(d) not enough information to decode
MTH 245 Calculus I
Test 3C (Sections 3.8 to 3.10) Fall 2007
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1. (2+2 points) Find the following limits.
(a) limx tan1 x
Solution: limx tan1 x =
2
(b) limx1+ sin1 x
Solution: limx1+ sin1 x =
2
2. (3+3+3+3 points) Find t
MTH 245 Calculus I
Test 3C - (Sections 3.8 to 3.10) Fall 2007
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1. (2+2 points) Find the following limits.
(a) limx tan1 x
(b) limx1+ sin1 x
2. (3+3+3+3 points) Find the derivatives of the following functions.
(a) y = sin1 (x2 )
(b
MTH 245 Calculus I
Exam 4 (Chapter 4) Fall 2007
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1. (3 points) Find the absolute maximum and minimum values of the function f (x) = x2 8 ln x on the interval
[1, 3]. (ln 2 0.69 and ln 3 1.1)
8
Solution: f 0 (x) = 2x x .
MTH 245 Calculus I
Test 3B (Sections 3.5 to 3.7) Fall 2007
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1. (2+2+2+2 points) Find the derivatives of the following functions
(a) y = (3x 7)18
Solution:
d
(3x 7)
dx
= 18(3x 7)17 3
= 54(3x 7)17
y0
= 18(3x 7)17
(b) y =
MTH 245 Calculus I
Test 3A (Sections 3.1 to 3.4) Fall 2007
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1
1. (4 points) Use the denition of derivatives to nd the derivative of f (x) = x . Also nd f 0 (2).
Solution:
f (x + h) f (x)
h0
h
1
1
x
= lim x+h
h0
h
f 0 (x)
MTH 245 Calculus I
Chapter 4
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1. Find the absolute maximum and minimum values of each function on the given interval.
(a) f (x) = x3 3x,
2 x 2
0
Solution: f (x) = 3x2 3 = 3(x2 1) = 3(x 1)(x + 1). Thus,
f 0 (x) = 0
3(x 1
MTH 245 Calculus I
Test 1 (Chapter 1) Fall 2007
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1. (2 + 2 points) Find the domains of the following functions.
(a) f (x) = x2 + 5
Solution: Dom(f ) = (, ), i.e., all real numbers.
(b) g (x) = x 1
Solution: Dom(g ) = [1,
MTH 245 Calculus I
Test 2 (Chapter 2) Fall 2007
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1. (2 + 2 points) Find the average rate of change of the function over the given interval.
(a) f (x) = x2 3;
[1, 4]
Solution: Average rate of change of f (x) over the inte
MTH 141 Applied Calculus
Exam 2 - Chapter 2 (Sections 2.1 to 2.4)
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1. (5 points) Let f (x) = x2 + 5. Use the limit denition to nd the derivatives of f.
Solution:
)
limx0 f (x+xxf (x)
(x+x)2 +5(x2 +5)
limx0
x 2
2
2
x
limx
MTH 141 Applied Calculus
Exam 3 - Chapter 2 (Sections 2.5 to 2.8)
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1. (3 points) Let y = (2x2 5 x + 6)6 . Find f (x) and g (x) such that y = f (g (x).
Solution: f (x) = x6 and g (x) = 2x2 5 x + 6.
2. (3+3+3 points) Find
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.1 to 3.4)
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1. (3 + 4 points) Find the critical numbers and the open intervals on which the function is increasing or
decreasing.
(a) g (x) = x2 2x + 3
Solution: The
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.5 to 3.7)
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1. (3.5 points) Find the number of units x that produces a maximum revenue R, where R = 48x2 0.02x3
Solution:
R = 48x2 0.02x3
R0 = 96x 0.06x2
R00 = 96 0.
MTH 141 Applied Calculus
Exam 1 (Chapter 1) - Fall 2006
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1. (2 + 2 points) Find the x and y intercepts of the following graphs.
(a) y = x2 4x + 3
Solution: To nd the x-intercept, put y = 0. So
x2 4x + 3 = 0
(x 3)(x 1) =
MTH 141 Applied Calculus
Exam 2 - Chapter 2 (Sections 2.1 to 2.4)
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1. (5 points) Let f (x) = 2x 7. Use the limit denition to nd the derivatives of f.
Solution:
f 0 (x) =
=
=
=
=
f (x + x) f (x)
x
2(x + x) 7 (2x 7)
lim
x0
MTH 141 Applied Calculus
Exam 1 (Chapter 1) - Spring 2007
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1. (1.5 + 1.5 + 2 points) Find the domains of the following functions. Write your answer in the interval
form.
(a) f (x) = x2 3x + 4
Solution: f (x) is a polynom
MTH 141 Applied Calculus
Exam 3 - Chapter 2 (Sections 2.5 to 2.7)
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1. (3 points) Let y = (x5 + 7x2 + 3 x3 + 6)8 . Find f (x) and g (x) such that y = f (g (x).
Solution: f (x) = x8 and g (x) = x5 + 7x2 + 3 x3 + 6.
2. (3+3
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.1 to 3.4)
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1. (3 + 4 points) Find the critical numbers and the open intervals on which the function is increasing or
decreasing.
(a) g (x) = x2 + 3x 9
Solution: The
MTH 141 Applied Calculus
Exam 3 - Chapter 3 (Sections 3.5 to 3.7)
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1. (4.5 points) Find the number of units x that produces a maximum revenue R, where R = 400x x2
Solution:
R = 400x x2
R0 = 400 2x
R00 = 2
So
R0 = 0
400