It is incredible how far calculators have come since my parents were in college, which was when the square root key came out. Calculators since then have evolved into machines that can take natural logarithms, sines, cosines, arcsines, and so on. The funny thing is that calculators have not gotten any "smarter" since then. In fact, calculators are still basically limited to the four basic operations: addition, subtraction, multiplication, and division! So what is it that allows calculators to evaluate logs, trigonometric functions, and exponents? This ability is due in large part to the Taylor series, which has allowed mathematicians (and calculators) to approximate functions,such as those given above, with polynomials. These polynomials, called Taylor Polynomials, are easy for a calculator manipulate because the calculator uses only the four basic arithmetic operators.

So how do mathematicians take a function and turn it into a polynomial function? Lets find out. First, lets assume that we have a function in the form y= f(x) that looks like the graph below.

We'll start out trying to approximate function values near x=0. To do this we start out using the lowest order polynomial, f0(x)=a0, that passes through the y-intercept of the graph (0,f(0)). So f(0)=ao.

Next, we see that the graph of f1(x)= a0 + a1x will also pass through x= 0, and will have the same slope as f(x) if we let a0=f1(0).

Now, if we want to get a better polynomial approximation for this function, which we do of course, we must make a few generalizations. First, we let the polynomial fn(x)= a0 + a1x + a2x2 + ... + anxn approximate f(x) near x=0, and let this functions first n derivatives match the the derivatives of f(x) at x=0. So if we want to make the derivatives of fn(x) equal to f(x) at x=0, we have to chose the coefficients a0 through an properly. How do we do this? We'll write down the polynomial and its...

...hp calculators
HP 50g Using TaylorSeries
The menu LIMITS AND SERIES Practice using Taylorseries
hp calculators HP 50g Using TaylorSeries The menu LIMITS AND SERIES The menu LIMITS AND SERIES contains commands related to limits. To access it you press !Ö. You are presented then the calculus menu as a CHOOSE box:
Figure 1
Its second menu item is 2.LIMITS AND SERIES... You can use such CHOOSE boxes much like menus of computer applications. You can move the selection using the arrow keys. You can also jump to a certain menu item by typing the first few letters of the command or the number at the left of the menu item. Pressing the `key or the menu key %OK% will execute the selected item. In this CHOOSE box you press 2 to select 2.LIMITS AND SERIES.. and then ` or %OK% to display the menu:
Figure 2
The command DIVPC needs two polynomials and an integer. It returns the increasing power quotient of the two polynomials up to an order indicated by the integer. The command lim takes an algebraic object and an equation of the form variable=expression. It returns the limit of the algebraic expression when the given variable approaches the expression at the right hand side of the equation. The command SERIES needs an algebraic expression, and equation of the form...

...(x).
5a.
When y = sin (1), y = 0.841. Using the Taylorseries with two terms, y = 0.830.
When y = sin (5), y = -0.958. Using the Taylorseries with two terms, y = - 15.8.
When y = cos (1), y = 0.540. Using the Taylorseries with two terms, y= 0.500.
When y = cos (5), y = 0.284. Using the Taylorseries with two terms, y = - 11.5.
By using the formula, Percentage Error =
Percentage Error for Taylorseries with two terms =
= 1377.18 % ≈ 1380 % (3sf)
5b.
When y = sin (1), y = 0.841. Using the Taylorseries with three terms, y = 0.842.
When y = sin (5), y = -0.958. Using the Taylorseries with three terms, y = 10.2.
When y = cos (1), y = 0.540. Using the Taylorseries with three terms, y = 0.542.
When y = cos (5), y = 0.284. Using the Taylorseries with three terms, y = 14.5.
Percentage Error for Taylorseries with two terms=
= 1492.80% ≈ 1490% (3sf)
5c.
When y= sin (1), y = 0.841. Using the Taylorseries with four terms, y= 0.841.
When y = sin (5), y = -0.958. Using the Taylorseries with four terms, y= -5.29.
When y = cos (1), y = 0.540. Using the Taylor...

...Interpretation and analysis of Gifts to the Dark Gods by Mary McCluskey
by Nanna March 2013.
When you hear the word “addiction” you will instantly think of addiction as a continued use of a mood altering substance, such as alcohol or drugs. That is the kind of addiction, people mostly hear and talk about.
But addiction can also be something you develop through time, a consequence of things you might have experienced or simply just a fun little habit, which has gotten out of control.
When I first laid eyes on the title of this story, I suddenly thought, that it might be a crucial horror story, about a person who sacrificed poor victims to some Satanic God, whom the main character believed in.
And I wasn’t that wrong. Surely, the story is not about a cold-blooded murder, who murders to please his or her Master, but it still is about a person, who collects things – material things, not dead people – so she can sacrifice them to the dark gods, so they will leave her alone and not hurt her.
If you try to look at Helen as a person who knows her, but doesn’t know her dark secret, you’d probably think of her as the woman who has everything. She has a lovely, strong husband, some happy children and a job where she gets to help bewildered teenagers. The family is a family of virtue and wealth. Her husband is a lawyer; therefore he values morality and legality. He’s a man of principle of firm opinions. He’s the...

...Integrated Marketing
Mengxin Li
Sep 20th, 2014
Analysis of Ann Taylor
5C’s Analysis
Customer
Target: 30’s married working mother, 2 children combined income $75~150K. Formal suit and blouse.
Need: The capital of appropriate attire for professional women in the big city.
Retails: There are 261 Ann Taylor stores and 113 Ann Taylor Factory stores in US as of August 2, 2014.
Retail Channels: Customers can get information through Internet, official website, direct email, advertisement at the store, coupon, catalog, magazine etc.
Need & preference change: the cloth is also for women who out of grad school or out of the Peace Corps or returning from the maternity leave that was going to last four months and somehow lasted five years.
Trends: Due to the US economic uncertainty, people still looking for a good cloth but a low price. However, more and more companies are recruiting women at work, making more working women need professional attire. This is the future customer’s need that Ann Taylor could satisfy it.
Company (SWOT Analysis)
I. Strength
Geographical Advantage: Stores in 47 US states + Reliance on China’s
Brand Image: the capital of appropriate attire. Professional & succeeding.
Reputation: Strong brand identity and well established within the USA. Celebrity attention through Kate Middleton.
Human Resource: Hire a full management staff (Marketing, Operations, Design, Finance) to...

...management is a theory focusing on optimizing and simplifying jobs to efficiently increase productivity. It is also called Taylorism, based on the US engineer Frederick Winslow Taylor (1856-1915) who published The Principles of Scientific Management in 1909, where he believed scientifically optimizing the working way was more productive than making labour work as hard as they could.
One of the essential elements of Taylor’s Philosophy is scientific decision making (Edwin A. Locke, 1982, pp.14-22), which is proposed in contrast to the traditional unscientific management and rule of thumb. Another important element of Taylor’s Philosophy is to advocate the mental revolution and the interest consistency between the labour and manager.
Frederick Winslow Taylor, the classical managerialist of America, developed the scientific management in the early of 20th century. Therefore, people regarded him as the father of scientific management and also named this thought Taylorsim, named after Frederick Winslow Taylor. His theory is influencing and accepted in modern management as well.
It has a micro-approach, which is focusing on determining and optimizing the productivity of individual jobs rather than overall organization (Bruno Dyck，Mitchell Neubert,2009,p.39), because it is restricted to factory only. Since Taylor stranded from the supervisory viewpoint and tried to increase productivity at operation level, he spent many...

...Earth: Our Gift From God
Brooklynn McMurray
Liberty University
Abstract
This paper presents a Toulmin model argument for the care and usage of the Earth and its natural resources as dictated by God in the Holy Bible (NIV). The Old Testament provides many guidelines for man to live fruitfully on Earth. Because it was made by God and given to us, we must follow the guidelines that he has set forth in the care and preservation of our planet.
Earth: Our Gift From God
Before God created man, he created the heavens and the Earth. Anyone who has read Genesis can plainly see that Earth was created by God as a place for man to dwell. However, God didn’t just give us shelter and leave us to our own devices. God made the Earth specifically so it could feed us and nurture us. Genesis 1:29 states, “And God said, ‘Behold, I have given you every herb bearing seed, which is upon the face of all the Earth, and every tree, in which is the fruit of a tree yielding seed; to you it shall be for meat’.” Clearly God meant for the Earth to sustain man. Because God created the Earth for us, we must take care of our environment.
When God created the Earth, he had all of our needs in mind. We are mortal, and therefore need many things. Our rivers and springs provide the water we drink. Our...

...amazing gifts and talents. Having these extraordinary talents makes others realize how special that person truly is because of how much talent they have and how well they execute that talent. For example, a professional athlete is a person who uses their gift as a talent. Lebron James is one of the most gifted and talented athletes on the planet because of his size, speed, and agility. He is known as the best basketball player in the world because he works harder and harder everyday to be the best he can be and overall is gifted at the sport of basketball. Others have a gift of telling whether a person is hurting not in the physical way but in an emotional way. They have the ability of making people feel better and really understanding the problems they might have going on in their life. Thats a very important gift to have. So is a gift a talent or a purpose? Having a talent means that you're using your gift to your own advantage. However, using a gift for a purpose can be beneficial to others.
There is no actual time when one finds out if they have a talent or purpose. Throughout the years of a persons life, answering that question gets easier because one starts to get an idea of how they want to use their gift, if they want to use their gift to their own advantage or use their gift for a purpose by helping others. A good example of...

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