In the first term of my Calculus, I had a hard time to review all my previous Math subjects, like Trigonometry and Algebra. I don’t have any idea in Calculus; I just know that it’s harder and more complicated than my previous Math subjects. After the midterm of this Semester I somehow know what Calculus for is, I learned that Differential Calculus can be use in finding the change in ratio. I also know that Calculus can be use to find the maximum and minimum rate of objects. It can also apply in other situation that involve changing and math. Using the concept of function derivatives, it studies the behavior and rate on how different quantities change. Using the process of differentiation, the graph of a function can actually be computed, analyzed, and predicted.

Though it is complicated to use well, calculus does have a lot of practical uses - uses that you probably won't comprehend at first. The most common practical use of calculus is when plotting graphs of certain formulae or functions. Using methods such as the first derivative and the second derivative, a graph and its dimensions can be accurately estimated. These 2 derivatives are used to predict how a graph may look like, the direction that it is taking on a specific point, the shape of the graph at a specific point (if concave or convex), just to name a few. When do you use calculus in the real world? In fact, you can use calculus in a lot of ways and applications. Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts. Among the physical concepts that use concepts of calculus include motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. In fact, even advanced physics concepts including electromagnetism and Einstein's theory of...

...Calculus
is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem ofcalculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-definedlimit. Calculus has widespread uses in science, economics, and engineering and can solve many problems that algebra alone cannot.
Calculus is concerned with comparing quantities which vary in a non-linear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If quantities are continually changing, we need calculus to study what is going on.
BRANCHES OF CALCULUSCalculus is concerned with comparing quantities which vary in a non-linear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If...

...How the calculus was invented?
Calculus, historically known as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Ideas leading up to the notions of function, derivative, and integral were developed throughout the 17th century, but the decisive step was made by Isaac Newton and Gottfried Leibniz. Publication of Newton's main treatises took many years, whereas Leibniz published first (Nova methodus, 1684) and the whole subject was subsequently marred by a priority dispute between the two inventors of calculus.
Greek mathematicians are credited with a significant use of infinitesimals. Democritus is the first person recorded to consider seriously the division of objects into an infinite number of cross-sections, but his inability to rationalize discrete cross-sections with a cone's smooth slope prevented him from accepting the idea. At approximately the same time, Elea discredited infinitesimals further by his articulation of the paradoxes which they create.
Antiphon and later Eudoxus are generally credited with implementing the method of exhaustion, which made it possible to compute the area and volume of regions and solids by breaking them up into an infinite number of recognizable shapes.
Archimedes of Syracuse developed this method further, while also inventing heuristic methods which resemble modern day concepts somewhat. (See...

...
Remember that people who are not familiar with your handwriting will read what you write. Try to write or print so that what
you are writing is legible to those readers.
Important Reminders:
A pencil is required for the essay. An essay written in ink will receive a score of zero.
Do not write your essay in your test book. You will receive credit only for what you write on your
answer sheet.
An off-topic essay will receive a score of zero.
If your essay does not reflect your original and individual work, your test scores may be canceled.
The supervisor will tell you how much an essay on theto write an essay on the topic assigned below.
You have twenty-five minutes to write time you have topic assigned below.
Think carefully about the issue presented in the following excerpt and the assignment below.
Often we see people who persist in trying to achieve a particular goal, even when all the
evidence indicates that they will be unlikely to achieve it. When they succeed, we consider
them courageous for having overcome impossible obstacles. But when they fail, we think of
them as headstrong, foolhardy, and bent on self-destruction. To many people, great effort is
only worthwhile when it results in success.
Adapted from Gilbert Brim, “Ambition”
Assignment:
Is the effort involved in pursuing any goal valuable, even if the goal is not reached? Plan and write an essay in
which you develop your point of view on this issue. Support your position...

...Marketing: A Field of Superb Minds
A deep realization about marketing begins its existence when I was browsing on the Internet. An author named Seth Godin captures my oblivious being in view of marketing with an aphorism that goes this way, “marketing is a contest for people’s attention”. This line must be too short to consider but it carries a lot of denotations which could be branched out to many ideas. Thinking, with respect to my instructor’s introduction of Marketing Management, I was near to set store by shifting my present course into that course, his field of expertise. But he, himself alone enlightened me enough to consider that he was just “marketing” the course.
As I was going-over the lecture done through online, I can say, marketing is interesting. Like what Godin defined, it is a contest, so it is a battle of creative minds to produce and innovate products, services, ideas, places, even experiences and many more. I find these marketers (the people who seek response from another party) brilliant for they possess superb brainpower to make the marketed things more attention-grabbing thus creates a greater number of customers to buy. While the country is always seeking out for demands, the marketers have to pursue to influence the level, timing and composition of demand to meet the objectives. They should mount and maintain organization by keeping and following the marketing system wherein the...

...SOLUTIONS TO SUGGESTED PROBLEMS FROM THE TEXT PART 2
3.5 2 3 4 6 15 18 28 34 36 42 43 44 48 49 3.6 1 2 6 12 17 19 23 30 31 34 38 40 43a 45 51 52 1 4 7 8 10 14 17 19 20 21 22 26 r’(θ) = cosθ – sinθ 2 2 cos θ – sin θ = cos2θ z’= -4sin(4θ) -3cos(2 – 3x) 2 cos(tanθ)/cos θ f’(x) = [-sin(sinx)](cosx) -sinθ w’ = (-cosθ)e y’ = cos(cosx + sinx)(cosx – sinx) 2 T’(θ) = -1 / sin θ x q(x) = e / sin x F(x) = -(1/4)cos(4x)
(a) dy/dt = -(4.9π/6)sin(πt/6) (b) indicates the change in depth of water (a) Graph at end (b) Max on 1 July; 4500; yes; 1 Jan (c) pos 1 April; neg 1 Oct (d) 0 2 2 2 (a) a cosθ + √l – a sin θ (b) i: -2a cm/sec 2 2 2 ii: -a√2 – a / (√l – a /2 cm/sec
28 36 37 42 52a 52b 1 2 4b 5 8 13 17 26a 29 39 41 1 2 3 17 22 29 36 44a 46 49 2 5 8 10 14 16b 21 25 26 27 5.2 1 6 8 10 14
Sketch at end Sketch at the end
x = 0: not max/min x = 3/7: local max x = 1: local min
4.2
-1/3 g decreasing near x = x0 g has local min at x1 Sketch at end Sketch at end x = 4; y = 57
Max: 20 at x = 1 Min: -2 at x = -1; x = 8 Max: 2 at x = 0; x = 3 Min: 16 at x = -1; x = 2 (a) f(1) local min; f(0), f(2) local max (b) f(1) global min; f(2) global max
Global min = 2 at x = 1, No global max D=C r = 3B/(2A) Sketch at end Sketch at end. x = L/2 x = 2a Min: -2amps; Max: 2 amps
(a) xy + πy /8 (b) x + y + πy/2 (c) x = 100/(4 + π); y = 200/(4 + π)
2
2t / (t + 1) 1 / (x – 1) cosα/sinα (lnx) + 1 e . 1/x 1 -sin (lnt) / t 2 2 / (√1 – 4t ) 1 / t lnt 2 1 / (1 + 2u + 2u ) 0.8 -1 ‹ x ‹ 1 1 / ((ln...

...1. Physical Properties of Water and Ice
1. Molecular Weight:
A. 18.01528 g/mol
Water, Molar mass
Triple Point
The temperature and pressure at which solid, liquid, and gaseous water coexist in equilibrium is called the triple point of water. This point is used to define the units of temperature (the kelvin, the SI unit of thermodynamic temperature and, indirectly, the degree Celsius and even the degree Fahrenheit).
As a consequence, water's triple point temperature is a prescribed value rather than a measured quantity.
The triple point is at a temperature of 273.16 K (0.01 °C) by convention, and at a pressure of 611.73 Pa. This pressure is quite low, about 1⁄166 of the normal sea level barometric pressure of 101,325 Pa. The atmospheric surface pressure on planet Mars is 610.5 Pa, which is remarkably close to the triple point pressure. The altitude of this surface pressure was used to define zero-elevation or "sea level" on that planet.[33]
Density of water and ice
Density of ice and water as a function of temperature
Density of liquid water
Temp (°C)
Density (kg/m3)[20][21]
+100
958.4
+80
971.8
+60
983.2
+40
992.2
+30
995.6502
+25
997.0479
+22
997.7735
+20
998.2071
+15
999.1026
+10
999.7026
+4
999.9720
0
999.8395
−10
998.117
−20
993.547
−30
983.854
The values below 0 °C refer to supercooled water.
The density of water is approximately one gram per cubic centimeter. It is dependent on its temperature, but the...

...The Simple Ledger: Ledger Accounts
You will now learn the system used to maintain an up to date financial position.
They use an account and ledger.
Account:
Page specially used to record financial changes
There is one account for each different item affecting the financial position. (Bank, equipment, automobile…)
Ledger:
All the accounts together are called the ledger
Group or file of accounts
Used to record business transaction and keep track of the balances in each specific account
If you wanted to know how much cash the business has to write a cheque, you would look in the ledger (Cash Account)
If you wanted to know how much the business owes on a bank loan, you would look in the ledger (Bank Loan Account)
A ledger can be prepared in different ways (cards, looseleaf ledger, computer system)
T-account:
Simple type of account. (A quick and easy way to track what is happening in each account)
Accounting form we use to keep track of the specific balance in an account
Shaped like a “T”
The formal account, the one actually used in business, will be introduced at a later time.
Important Features of Ledger Accounts
1. Each individual balance sheet item is given its own specially divided page with the name of item at the top (for now think of each “T” as a page)
Each of these pages is called an account
You must learn to call each one by name. i.e., cash account, bank loan account, and so on.
2. The dollar figure for each item is...

...Sustainability and Calculus
Introduction and Preview
Calculus is all about change. Calculus provides the mathematical tools to examine important questions about dynamic behavior; e.g. how fast is the world population increasing? If we continuously release a pollutant into a lake at a known rate, what's the total amount of pollutant that will be dumped into the water in the next five years? How long will the nonrenewable supplies of coal and oil last if we maintain the current per capita use but population continues to grow? How long will supplies last if industrialization and a "rising standard of living" push per capita usage ever higher? If we disturb the natural population dynamics of a salmon species by fishing, how should we regulate our removal of fish to provide a maximal sustainable yield in the future?
Although we will study many different applications of calculus in this introductory course, we will place a particular emphasis on the problem of sustainability.
Sustainability means meeting the needs of the present without compromising the ability of future generations to meet their own needs.
Our definition of sustainability comes from the 1987 publication Our Common Future by the United Nations World Commission on Environment and Development (also known as the Brundtland commission after its chair, Norwegian diplomat Gro Harlem Brundtland)...

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