Current File : /var/www/html/sljcon/public/o23k1sc/cache/e57776b4def259ea7f00a1253957ae68
a:5:{s:8:"template";s:9951:"<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<meta content="width=device-width, initial-scale=1" name="viewport"/>
<title>{{ keyword }}</title>
<link href="https://fonts.googleapis.com/css?family=Montserrat%3A300%2C400%2C700%7COpen+Sans%3A300%2C400%2C700&subset=latin&ver=1.8.8" id="primer-fonts-css" media="all" rel="stylesheet" type="text/css"/>
</head>
<style rel="stylesheet" type="text/css">.has-drop-cap:not(:focus):first-letter{float:left;font-size:8.4em;line-height:.68;font-weight:100;margin:.05em .1em 0 0;text-transform:uppercase;font-style:normal}.has-drop-cap:not(:focus):after{content:"";display:table;clear:both;padding-top:14px}html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}body{margin:0}aside,footer,header,nav{display:block}a{background-color:transparent;-webkit-text-decoration-skip:objects}a:active,a:hover{outline-width:0}::-webkit-input-placeholder{color:inherit;opacity:.54}::-webkit-file-upload-button{-webkit-appearance:button;font:inherit}body{-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}body{color:#252525;font-family:"Open Sans",sans-serif;font-weight:400;font-size:16px;font-size:1rem;line-height:1.8}@media only screen and (max-width:40.063em){body{font-size:14.4px;font-size:.9rem}}.site-title{clear:both;margin-top:.2rem;margin-bottom:.8rem;font-weight:700;line-height:1.4;text-rendering:optimizeLegibility;color:#353535}html{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}*,:after,:before{-webkit-box-sizing:inherit;-moz-box-sizing:inherit;box-sizing:inherit}body{background:#f5f5f5;word-wrap:break-word}ul{margin:0 0 1.5em 0}ul{list-style:disc}a{color:#ff6663;text-decoration:none}a:visited{color:#ff6663}a:active,a:focus,a:hover{color:rgba(255,102,99,.8)}a:active,a:focus,a:hover{outline:0}.has-drop-cap:not(:focus)::first-letter{font-size:100px;line-height:1;margin:-.065em .275em 0 0}.main-navigation-container{width:100%;background-color:#0b3954;content:"";display:table;table-layout:fixed;clear:both}.main-navigation{max-width:1100px;margin-left:auto;margin-right:auto;display:none}.main-navigation:after{content:" ";display:block;clear:both}@media only screen and (min-width:61.063em){.main-navigation{display:block}}.main-navigation ul{list-style:none;margin:0;padding-left:0}.main-navigation ul a{color:#fff}@media only screen and (min-width:61.063em){.main-navigation li{position:relative;float:left}}.main-navigation a{display:block}.main-navigation a{text-decoration:none;padding:1.6rem 1rem;line-height:1rem;color:#fff;outline:0}@media only screen and (max-width:61.063em){.main-navigation a{padding:1.2rem 1rem}}.main-navigation a:focus,.main-navigation a:hover,.main-navigation a:visited:hover{background-color:rgba(0,0,0,.1);color:#fff}body.no-max-width .main-navigation{max-width:none}.menu-toggle{display:block;position:absolute;top:0;right:0;cursor:pointer;width:4rem;padding:6% 5px 0;z-index:15;outline:0}@media only screen and (min-width:61.063em){.menu-toggle{display:none}}.menu-toggle div{background-color:#fff;margin:.43rem .86rem .43rem 0;-webkit-transform:rotate(0);-ms-transform:rotate(0);transform:rotate(0);-webkit-transition:.15s ease-in-out;transition:.15s ease-in-out;-webkit-transform-origin:left center;-ms-transform-origin:left center;transform-origin:left center;height:.45rem}.site-content:after,.site-content:before,.site-footer:after,.site-footer:before,.site-header:after,.site-header:before{content:"";display:table;table-layout:fixed}.site-content:after,.site-footer:after,.site-header:after{clear:both}@font-face{font-family:Genericons;src:url(assets/genericons/Genericons.eot)}.site-content{max-width:1100px;margin-left:auto;margin-right:auto;margin-top:2em}.site-content:after{content:" ";display:block;clear:both}@media only screen and (max-width:61.063em){.site-content{margin-top:1.38889%}}body.no-max-width .site-content{max-width:none}.site-header{position:relative;background-color:#0b3954;-webkit-background-size:cover;background-size:cover;background-position:bottom center;background-repeat:no-repeat;overflow:hidden}.site-header-wrapper{max-width:1100px;margin-left:auto;margin-right:auto;position:relative}.site-header-wrapper:after{content:" ";display:block;clear:both}body.no-max-width .site-header-wrapper{max-width:none}.site-title-wrapper{width:97.22222%;float:left;margin-left:1.38889%;margin-right:1.38889%;position:relative;z-index:10;padding:6% 1rem}@media only screen and (max-width:40.063em){.site-title-wrapper{max-width:87.22222%;padding-left:.75rem;padding-right:.75rem}}.site-title{margin-bottom:.25rem;letter-spacing:-.03em;font-weight:700;font-size:2em}.site-title a{color:#fff}.site-title a:hover,.site-title a:visited:hover{color:rgba(255,255,255,.8)}.hero{width:97.22222%;float:left;margin-left:1.38889%;margin-right:1.38889%;clear:both;padding:0 1rem;color:#fff}.hero .hero-inner{max-width:none}@media only screen and (min-width:61.063em){.hero .hero-inner{max-width:75%}}.site-footer{clear:both;background-color:#0b3954}.footer-widget-area{max-width:1100px;margin-left:auto;margin-right:auto;padding:2em 0}.footer-widget-area:after{content:" ";display:block;clear:both}.footer-widget-area .footer-widget{width:97.22222%;float:left;margin-left:1.38889%;margin-right:1.38889%}@media only screen and (max-width:40.063em){.footer-widget-area .footer-widget{margin-bottom:1em}}@media only screen and (min-width:40.063em){.footer-widget-area.columns-2 .footer-widget:nth-child(1){width:47.22222%;float:left;margin-left:1.38889%;margin-right:1.38889%}}body.no-max-width .footer-widget-area{max-width:none}.site-info-wrapper{padding:1.5em 0;background-color:#f5f5f5}.site-info-wrapper .site-info{max-width:1100px;margin-left:auto;margin-right:auto}.site-info-wrapper .site-info:after{content:" ";display:block;clear:both}.site-info-wrapper .site-info-text{width:47.22222%;float:left;margin-left:1.38889%;margin-right:1.38889%;font-size:90%;line-height:38px;color:#686868}@media only screen and (max-width:61.063em){.site-info-wrapper .site-info-text{width:97.22222%;float:left;margin-left:1.38889%;margin-right:1.38889%;text-align:center}}body.no-max-width .site-info-wrapper .site-info{max-width:none}.widget{margin:0 0 1.5rem;padding:2rem;background-color:#fff}.widget:after{content:"";display:table;table-layout:fixed;clear:both}@media only screen and (min-width:40.063em) and (max-width:61.063em){.widget{padding:1.5rem}}@media only screen and (max-width:40.063em){.widget{padding:1rem}}.site-footer .widget{color:#252525;background-color:#fff}.site-footer .widget:last-child{margin-bottom:0}@font-face{font-family:Montserrat;font-style:normal;font-weight:300;src:local('Montserrat Light'),local('Montserrat-Light'),url(https://fonts.gstatic.com/s/montserrat/v14/JTURjIg1_i6t8kCHKm45_cJD3gnD-w.ttf) format('truetype')}@font-face{font-family:Montserrat;font-style:normal;font-weight:400;src:local('Montserrat Regular'),local('Montserrat-Regular'),url(https://fonts.gstatic.com/s/montserrat/v14/JTUSjIg1_i6t8kCHKm459Wlhzg.ttf) format('truetype')}@font-face{font-family:Montserrat;font-style:normal;font-weight:700;src:local('Montserrat Bold'),local('Montserrat-Bold'),url(https://fonts.gstatic.com/s/montserrat/v14/JTURjIg1_i6t8kCHKm45_dJE3gnD-w.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:300;src:local('Open Sans Light'),local('OpenSans-Light'),url(https://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UN_r8OUuhs.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:400;src:local('Open Sans Regular'),local('OpenSans-Regular'),url(https://fonts.gstatic.com/s/opensans/v17/mem8YaGs126MiZpBA-UFVZ0e.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:700;src:local('Open Sans Bold'),local('OpenSans-Bold'),url(https://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UN7rgOUuhs.ttf) format('truetype')}</style>
<body class="custom-background wp-custom-logo custom-header-image layout-two-column-default no-max-width">
<div class="hfeed site" id="page">
<header class="site-header" id="masthead" role="banner">
<div class="site-header-wrapper">
<div class="site-title-wrapper">
<a class="custom-logo-link" href="#" rel="home"></a>
<div class="site-title"><a href="#" rel="home">{{ keyword }}</a></div>
</div>
<div class="hero">
<div class="hero-inner">
</div>
</div>
</div>
</header>
<div class="main-navigation-container">
<div class="menu-toggle" id="menu-toggle" role="button" tabindex="0">
<div></div>
<div></div>
<div></div>
</div>
<nav class="main-navigation" id="site-navigation">
<div class="menu-primary-menu-container"><ul class="menu" id="menu-primary-menu"><li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-home menu-item-170" id="menu-item-170"><a href="#">Home</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-172" id="menu-item-172"><a href="#">About Us</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-169" id="menu-item-169"><a href="#">Services</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-page current_page_parent menu-item-166" id="menu-item-166"><a href="#">Blog</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-171" id="menu-item-171"><a href="#">Contact Us</a></li>
</ul></div>
</nav>
</div>
<div class="site-content" id="content">
{{ text }}
</div>
<footer class="site-footer" id="colophon">
<div class="site-footer-inner">
<div class="footer-widget-area columns-2">
<div class="footer-widget">
<aside class="widget wpcw-widgets wpcw-widget-contact" id="wpcw_contact-4">{{ links }}</aside>
</div>
</div>
</div>
</footer>
<div class="site-info-wrapper">
<div class="site-info">
<div class="site-info-inner">
<div class="site-info-text">
2020 {{ keyword }}
</div>
</div>
</div>
</div>
</div>
</body>
</html>";s:4:"text";s:9353:" During the emergence of internet culture, individuals and organizations sometimes paid homage to the number e. In an early example, the computer scientist Donald Knuth let the version numbers of his program Metafont approach e. The versions are 2, 2.7, 2.71, 2.718, and so forth. The problem of de Montmort is to find the probability that none of the hats gets put into the right box. e {\displaystyle y=(x-e)/e} Value of e. Like pi, e is an irrational real number. Furthermore, the number of ways the hats can be placed into the boxes so that none of the hats are in the right box is n!/e (rounded to the nearest integer for every positive n). Each time the gambler plays the slots, there is a one in n chance of winning. The value of this maximum is 1.4446 6786 1009 7661 3365... (accurate to 20 decimal places). The value of n that maximizes the product of the lengths is then either[19]. e is an irrational number (it cannot be written as a simple fraction).. e is the base of the Natural Logarithms (invented by John Napier).. e is found in many interesting areas, so is worth learning about.. 1 It is assumed that the table was written by William Oughtred. [9] However, this did not contain the constant itself, but simply a list of logarithms calculated from the constant. This continued fraction for e converges three times as quickly:[citation needed]. What happens if the interest is computed and credited more frequently during the year? , and has inflection points at x = ±1. For other uses, see, "E (number)" redirects here. asked Feb 27 '12 at 0:03. Furthermore, using the laws for exponentiation. [23] This is a limiting case of Bernoulli's inequality. ) Google was also responsible for a billboard[42] BankingWe offer fast, cost-effective collateral value monitoring solutions for bank professionals. The special case with x = π is Euler's identity: from which it follows that, in the principal branch of the logarithm. x But the butler has not asked the identities of the guests, and so he puts the hats into boxes selected at random. It was the first number to be proved transcendental without having been specifically constructed for this purpose (compare with Liouville number); the proof was given by Charles Hermite in 1873. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Exponential values, returned as a scalar, vector, matrix, or multidimensional array. x The constraint of unit variance (and thus also unit standard deviation) results in the 1/2 in the exponent, and the constraint of unit total area under the curve / x [18], A stick of length L is broken into n equal parts. [13][14] Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons,[15] while the first appearance of e in a publication was in Euler's Mechanica (1736). Learn more about different mathematical constant and get the values for them to solve mathematical problems. Workflow SolutionsOur fast, cost-effective inspection workflow solutions can be used by both insurance carriers and inspection companies to streamline the inspection process. For example, how would I go about entering the value e^2 in R? [5] To 50 decimal places the value of e is: The first references to the constant were published in 1618 in the table of an appendix of a work on logarithms by John Napier. The result can be shown in multiple forms. Generally one is more comfortable with base 10 and even remember some result of log. {\displaystyle 1/x} ", First 10-digit prime found in consecutive digits of, "Google Entices Job-Searchers with Math Puzzle", https://en.wikipedia.org/w/index.php?title=E_(mathematical_constant)&oldid=991371378, Wikipedia indefinitely move-protected pages, Short description is different from Wikidata, Articles with unsourced statements from October 2017, Articles with unsourced statements from August 2020, Articles with unsourced statements from September 2018, Creative Commons Attribution-ShareAlike License, This page was last edited on 29 November 2020, at 18:26. Lettre XV. [25], The real number e is irrational. / [26] (See also Fourier's proof that e is irrational.). x Carpet and seat upholstery should be clean, and all power options should work. This is due both to the increased performance of computers and to algorithmic improvements. Let V be the least number n such that the sum of the first n observations exceeds 1: Then the expected value of V is e: E(V) = e.[29][30], The number of known digits of e has increased substantially during the last decades. There are many ways of calculating the value of e, but none of them ever give a totally exact answer, because e is irrational and its digits go on forever without repeating. e Our fast, cost-effective inspectionworkflow solutions can be used byboth insurance carriers and inspectioncompanies to streamline the inspectionprocess. e in terms of the exponential function can be deduced: where C is any real number, is the solution to the differential equation, The number e can be represented in a variety of ways: as an infinite series, an infinite product, a continued fraction, or a limit of a sequence. For n = 20, this is already approximately 1/2.79. This means that it cannot be written as a fraction, and that its decimal expansion goes on forever with no repeating block of numbers that continually repeats. The exponential function ex may be written as a Taylor series. Exact Form: 1 e2 1 e … David Arenburg. 2,173 9 9 gold badges 28 … Calculating the Value of e. There are several ways to calculate the value of e. Let's look at the historical development. {\displaystyle x^{-1}\ln x} If the interest is credited twice in the year, the interest rate for each 6 months will be 50%, so the initial $1 is multiplied by 1.5 twice, yielding $1.00 × 1.52 = $2.25 at the end of the year. ≥ We're proud to offer the only web-based estimatorthat is solely dedicated to farm and ranch structures. [proof] This function is symmetric around x = 0, where it attains its maximum value π The number e itself also has applications in probability theory, in a way that is not obviously related to exponential growth. 85.9k 14 14 gold badges 121 121 silver badges 176 176 bronze badges. Playing n times is modeled by the binomial distribution, which is closely related to the binomial theorem and Pascal's triangle. One way is to set the derivative of the exponential function ax equal to ax, and solve for a. Calculating. For real values of X in the interval (-Inf, Inf), Y is in the interval (0,Inf).For complex values of X, Y is complex. The natural logarithm of a number k > 1 can be defined directly as the area under the curve y = 1/x between x = 1 and x = k, in which case e is the value of k for which this area equals one (see image). ( It is the base of the natural logarithm. It turns out that these two solutions for a are actually the same: the number e. Other characterizations of e are also possible: one is as the limit of a sequence, another is as the sum of an infinite series, and still others rely on integral calculus. More generally, for the function. {\displaystyle \phi (x)} Using a Binomial Expansion. x For proof, the inequality Using a Binomial Expansion. Compounding weekly (n = 52) yields $2.692597..., while compounding daily (n = 365) yields $2.714567... (approximately two cents more). . ≥ e 2 = (2.718281828) 2 = 2.718281828 x 2.718281828 = 7.38906. e 3 = (2.718281828) 3 = 2.718281828 x 2.718281828 x 2.718281828 = 20.08554. e 4 = (2.718281828) 4 = 2.718281828 x 2.718281828 x 2.718281828 x 2.718281828 = 54.59815. In addition to exact analytical expressions for representation of e, there are stochastic techniques for estimating e. One such approach begins with an infinite sequence of independent random variables X1, X2..., drawn from the uniform distribution on [0, 1]. If n is very large (approaches infinity) the value of `(1+1/n)^n`approaches e. This is not an efficient way to find `e`. What will be the value of a single $5,000 investment foWhat will be the value of a single $5,000 investment for 10 years if the 5.0% interest is continuously compounded?r 10 years if the 5.0% interest It read "{first 10-digit prime found in consecutive digits of e}.com". , is: As the number n of guests tends to infinity, pn approaches 1/e. Another application of e, also discovered in part by Jacob Bernoulli along with Pierre Raymond de Montmort, is in the problem of derangements, also known as the hat check problem:[17] n guests are invited to a party, and at the door, the guests all check their hats with the butler, who in turn places the hats into n boxes, each labelled with the name of one guest. ";s:7:"keyword";s:12:"value of e^2";s:5:"links";s:1043:"<a href="http://sljco.coding.al/o23k1sc/what-does-a-school-nurse-do-in-a-primary-school-566a7f">What Does A School Nurse Do In A Primary School</a>,
<a href="http://sljco.coding.al/o23k1sc/long-eared-owl-interesting-facts-566a7f">Long-eared Owl Interesting Facts</a>,
<a href="http://sljco.coding.al/o23k1sc/oribe-serene-scalp-conditioner-566a7f">Oribe Serene Scalp Conditioner</a>,
<a href="http://sljco.coding.al/o23k1sc/masterbuilt-pellet-grill-cover-566a7f">Masterbuilt Pellet Grill Cover</a>,
<a href="http://sljco.coding.al/o23k1sc/certificate-in-engineering-566a7f">Certificate In Engineering</a>,
<a href="http://sljco.coding.al/o23k1sc/baltic-birch-plywood-windsor-ontario-566a7f">Baltic Birch Plywood Windsor Ontario</a>,
<a href="http://sljco.coding.al/o23k1sc/shredded-mexican-chicken-566a7f">Shredded Mexican Chicken</a>,
<a href="http://sljco.coding.al/o23k1sc/emporio-armani-perfume-566a7f">Emporio Armani Perfume</a>,
<a href="http://sljco.coding.al/o23k1sc/ski-dubai-mountain-thriller-566a7f">Ski Dubai Mountain Thriller</a>,
";s:7:"expired";i:-1;}
Mini Shell