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...

...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 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,...

...HP 10bII+ Financial Calculator User’s Guide
HP Part Number: NW239-90001 Edition 1, May 2010
i
Legal Notice
This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non-infringement and fitness for a particular purpose. In this regard, HP shall not be liable for...

...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,...

...management theory would be indicated below.
Taylor’s Philosophy
Scientific 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...

...
Critical Reading and Writing
Professor Yu
7 November 2013
A few people in this world are blessed with 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...

1162 Words |
3 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":32768278,"categoryName":"Fiction","categoryParentId":"17","currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":2,"pageRange":"1-2","totalPages":2}},"access":"premium","title":"Gods Gift to Calculators: the Taylor Series","additionalIds":[16,184,7,93],"additional":["Law","Law\/Intellectual Property","Education","Education\/Greek System"],"loadedPages":{"html":[],"text":[1,2]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Gods-Gift-To-Calculators-The-Taylor-2567.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"},"analytics":{"googleId":"UA-32718321-1"}}