...as ratios rather than lengths of lines. Another Astronomer from Sweden discovered logarithms, and then another large step in Trigonometry was made by Isaac Newton whom founded differential and integral calculus. The history of Trigonometry came about mainly due to the purposes of time keeping and astronomy.
Four different careers that use trigonometry are Sailors, Astronomy, Architects, and Surveyors. Sailors use trigonometry for geography and navigation. Sailors are known to have been using trigonometry for these reasons to determine their position when they were in the middle of the sea without any other means. Astronomers used Trigonometry to calculate the position of planets, it’s also used as the geographical concept of latitude and longitude, in which you can identify and locate any area in the world. An example of how Surveyors use Trigonometry is if you know two sides of a triangle, trig lets you find the third. So if you want to know the distance across a lake, measure two lines along the side of the lake such that they form a triangle with the line across the lake, and you can find the distance across all by using Trigonometry. Science and mathematics are themselves a field of application of trigonometry. Sciences and mathematics such as analytic geometry, calculus, dynamics, satellite launching, physics and chemistry are all enriched and enhanced by trigonometry. In architecture, trigonometry plays a huge role in the designing and...

...module3
ematology – Module3, Lecture 1
Slide 1
● The first type of blood cells that we will focus on are the erythrocytes, also called the
red blood cells. These are the cells that transport oxygen in the blood from the lungs
to the tissues. These cells also help transport some of the carbon dioxide from the
tissues to the lungs. The main function of erythrocytes, namely oxygen transport, is
carried out by the protein that makes up the majority of the protein composition of the
cell, hemoglobin. We will also be looking at how hemoglobin delivers oxygen, and
how many factors affect its affinity for oxygen. Lastly we will be looking at some
variations of hemoglobin, one variation of which is determined by the combination of
chains, and which occurs over the lifetime of an individual. The other variation is
based on which molecule binds to hemoglobin, and whether these variants are
functional or not.
Slide 2
● First, we will be looking at the molecular composition of the erythrocyte, mostly of the
plasma membrane and the area beneath it. The chemical composition largely
determines the functionality of the cell, whether it is fit to carry out its principal function
over its lifetime of 120 days, or it is not fit, in which case it is destroyed immediately.
● We will be looking at the metabolic processes that keep the cells alive. Mature red ...

...No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Pre-requisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
9. 10.
Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit, students will be able to: 1. describe the basic ideas concerning functions, their graphs, and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization problems; 4. relate the integral to the derivative; 5. use the integral to solve problems concerning areas.
11.
12.
Subject Synopsis: This unit covers topics on Functions and Models, Limits and Derivatives, Differentiation Rules, Applications of Differentiation and Integrals.
13.
Subject Outline and Notional Hours: Topic Learning Outcomes 1 L 4 T 1.5 P SL 6.25 TLT 11.75
Topic 1: Functions and Models
• • • • • • Functions Models and curve fitting...

...sentimental . . litigious
resolute . . polemical
steadfast . . acquiescent
(C) conjectural
8. African American poet Lucille Clifton writes in a
notably ------- style, achieving great impact in a
few unadorned words.
3. Electing not to stay in subordinate positions in large
firms, some attorneys -------, seeking more ------- and
independence elsewhere.
(A)
(B)
(C)
(D)
(E)
ignore . . universal
criticize . . visionary
condemn . . benevolent
denounce . . pragmatic
condone . . indulgent
6. The critic noted that the ------- tone that characterizes
much of the writer’s work stands in stark contrast to
his gentle disposition.
1. Women in the United States gained ------- long after
Black American men did, but Black citizens had
greater difficulty exercising their new voting rights.
(A) restitution
(B) suffrage
(D) initiatives
(E) levies
(C) prodigious
5. Because all members of this organization are
idealists, they ------- any assertion that political
enterprises should be purely -------.
Example:
(A)
(B)
(C)
(D)
(E)
(B) vestigial
(E) kinetic
(A) incantatory
(D) unstinting
compromise . . servility
persevere . . competence
acquiesce . . banality
resign . . autonomy
recant . . conformity
-3-
(B) economical
(C) disaffected
(E) evenhanded
The passages below are followed by questions based on their content; questions following a pair of related passages may also
be based on...

...Exam 3 Content
(Sections 3.7 - 3.11)
Solve problems using all derivatives learned thus far in the course,
but specifically:
1. Use logarithmic differentiation to find the derivative.
2. Use implicit differentiation.
3. Find the slope of a curve at a point and the tangent and normal lines at that point.
4. Find the value of the derivative of an inverse function for a given value of x.
5. Solve a related rates problem.
6. Find the linearization L(x) of a function for a given value of x.
...

...Name:
Date:
Graded Assignment
Checkup: Graphing Polynomial Functions
Answer the following questions using what you've learned from this unit. Write your responses in the space provided, and turn the assignment in to your instructor.
For problems 1 – 5, state the x- and y-intercepts for each function.
1.
x-intercept: (0, 0), (-4, 0), (0, 0)
y-intercept: (0, 0)
2.
x-intercept: (1, 0) (0, 0) (-4, 0)
y-intercept: (0, 4)
3.
x-intercept: (-1, 0) (0, 0) (0, 0)
y-intercept: (0, 0)
4.
x-intercept: (0, 0) (0, 0) (-25, 0)
y-intercept: (0, 0)
5.
x-intercept: (5, 0) (0, 0) (3, 0)
y-intercept: (0, -15)
For problems 6 – 10, describe the end behavior for each of the functions by writing a limit expression.
6.
lim f(x) = (infinity)
x -> (infinity)
7.
lim f(x) = - (infinity)
x -> (infinity)
8.
lim f(x) = - (infinity)
x -> (infinity)
9.
lim f(x) = (infinity)
x -> (infinity)
10.
lim f(x) = - (infinity)
x -> (infinity)
For problems 11 – 13, use the graphs to state the zeros for each polynomial function. State the multiplicity of any roots if the multiplicity is 2 or higher.
11.
Zeros: x = 0, x = 2
Multiplicity of 0 is 2.
12.
Zeros: x = -2, x = 2
Multiplicity of 2 is 2.
13.
Zeros: x = -0.5, x = 0, x = 0.5
No multiplicity higher than 1.
For problems 14 – 16, identify the extrema for each function. Classify each as a relative (local) or absolute (global) maximum or...

... _6_
2. _10_
3. _3_
Classify each expression as a polynomial or not. If the expression is a polynomial, name it according to its degree and its number of terms.
4.
Not a Polynomial
5.
Quintic Polynomial
6.
Not a Polynomial
7.
Not a Polynomial
Write the polynomial in standard form, then identify its leading coefficient and constant term.
8. Standard form: 11x^3 + 6x^2 + 2x
Leading coefficient: 11 Constant term: none/0
9. Standard form: x^4 – 11x^3 + 36x^2 + 5
Leading coefficient: 1 Constant term: 5
10. Standard form: x^4y + x^2y^2 + 7
Leading coefficient: 1 Constant term: 7
State the maximum possible number of "turns" in the graph of each polynomial.
11. Max. Possible Turns: 5 -1 = 4
12. Max. Possible Turns: 3 – 1 = 2
Complete the statements by filling in the blanks for each polynomial:
Polynomial
Right End Behavior
Left End Behavior
13.
As , positive infinity.
As , negative infinity.
14.
As , positive infinity.
As , positive infinity.
15.
As , negative infinity.
As , negative infinity.
16.
As , positive infinity.
As , negative infinity.
17.
As , positive infinity.
As , positive infinity.
18.
As , negative infinity.
As , positive infinity.
Match each polynomial with its graph:
19. __B__
20. __D__
21. __A__
22. __C__
A. B.
C. D.
Calculate each value using direct substitution or synthetic substitution....

...Name:
Date:
Graded Assignment
Checkup: Solving Polynomial Equations
Answer the following questions using what you've learned from this lesson. Write your responses in the spaces provided, and turn the assignment in to your instructor.
List all possible rational zeros for each polynomial function.
1.
-3, 2, 5
2.
-12, 17. 27
Use Descartes' rule of signs to describe the roots for each polynomial function.
3.
Two sign changes = Two or no positive roots
m(-x) = (-x)3 + 3(-x)2 – 18(-x) – 40
= -x + 3x + 18x - 40
Two sign changes = Two or no positive roots
4.
Three sign changes = Three or one positive roots
w(-x) = (-x)4 + 4(-x)3 – 7(-x)2 + 20(-x) - 21
= x – 4x – 7x – 20x – 21
No sign changes = No negative roots
Find an upper bound and a lower bound for the zeros of the following polynomial functions.
5.
Upper Bound: 8
Lower Bound: -6
6.
Upper Bound: 3
Lower Bound: 2
Factor each polynomial completely over the set of complex numbers.
7.
8.
9.
Write a polynomial that has the given numbers as roots.
10.
11.
Use the graph to guess one zero for the polynomial whose graph is shown. Then factor completely.
12.
13.
14. Solve the quadratic equation by the method of square roots:...