{"id":178038,"date":"2024-02-29T16:23:27","date_gmt":"2024-02-29T15:23:27","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=178038"},"modified":"2024-02-09T17:06:24","modified_gmt":"2024-02-09T16:06:24","slug":"limit-of-a-function-how-to-determine-it","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/limit-of-a-function-how-to-determine-it","title":{"rendered":"Limit of a function: how to determine it?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"178038\" class=\"elementor elementor-178038\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e99e799 e-flex e-con-boxed e-con\" data-id=\"e99e799\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d0420ee elementor-widget elementor-widget-heading\" data-id=\"d0420ee\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">All scientific disciplines are based on mathematics, and data science is no exception. When the problems to be solved are optimization problems, you need to know what the limit of a function is. In this article, you'll discover how to determine the limit of a function.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a6d6c90 e-flex e-con-boxed e-con\" data-id=\"a6d6c90\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b96e4e7 elementor-widget elementor-widget-heading\" data-id=\"b96e4e7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Limit: Definition<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fb11d22 elementor-widget elementor-widget-shortcode\" data-id=\"fb11d22\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">The limit of a function <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> is the value the function approaches when its argument approaches a certain value.<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-304af4e elementor-widget elementor-widget-shortcode\" data-id=\"304af4e\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Mathematically, we write <\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bbf09ae elementor-widget elementor-widget-shortcode\" data-id=\"bbf09ae\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim \\limits_{x \\to a} f(x) = l<\/span>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1aa6552 elementor-widget elementor-widget-shortcode\" data-id=\"1aa6552\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">We say that <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> tends towards <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> when <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> tends towards <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>.<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3d16e93 elementor-widget elementor-widget-shortcode\" data-id=\"3d16e93\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Depending on the case, <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> may be real numbers, or equal to <span class=\"katex-eq\" data-katex-display=\"false\">\\pm \\infty<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cb96ba6 e-flex e-con-boxed e-con\" data-id=\"cb96ba6\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-45dc947 elementor-widget elementor-widget-heading\" data-id=\"45dc947\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Limits of standard functions<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1317391 elementor-widget elementor-widget-heading\" data-id=\"1317391\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">- Real-valued finite limits\n<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b4d127c elementor-widget elementor-widget-shortcode\" data-id=\"b4d127c\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">For example, for <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = x^2<\/span>, the limit when <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> tends towards <span class=\"katex-eq\" data-katex-display=\"false\">2<\/span> is <span class=\"katex-eq\" data-katex-display=\"false\">2^2 = 4<\/span>.<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e6580a8 elementor-widget elementor-widget-heading\" data-id=\"e6580a8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">- Infinite limits\n<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-89f6adb elementor-widget elementor-widget-shortcode\" data-id=\"89f6adb\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">When the function is well defined at a real number <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> (it is said to be continuous at <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>), then the limit at <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> is exactly <span class=\"katex-eq\" data-katex-display=\"false\">f(a)<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c4005b5 elementor-widget elementor-widget-shortcode\" data-id=\"c4005b5\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">When the variable <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> takes on very large values (positively or negatively), we say that <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> tends towards more or less infinity. In this case, we distinguish between cases where <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> approaches a finite value and those where <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> moves away towards infinity. In the former case, <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> is said to converge, and in the latter, <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> to diverge.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-999a33a elementor-widget elementor-widget-shortcode\" data-id=\"999a33a\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Below is a table summarizing the limits of common functions at infinity.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df29982 elementor-hidden-desktop elementor-hidden-tablet elementor-widget elementor-widget-image\" data-id=\"df29982\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Limite-usuelle.png\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"Jam AWS: The playful learning platform from Amazon\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTY5NzgyLCJ1cmwiOiJodHRwczpcL1wvZGF0YXNjaWVudGVzdC5jb21cL2VuXC9maWxlc1wvMjAyM1wvMDhcL2F3cy1qYW0yLnBuZyJ9\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"640\" height=\"366\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/08\/aws-jam2.png\" class=\"attachment-full size-full wp-image-169782\" alt=\"A man and a woman are sitting in front of a laptop\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/08\/aws-jam2.png 640w, https:\/\/datascientest.com\/en\/files\/2023\/08\/aws-jam2-300x172.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-83abc62 elementor-widget elementor-widget-shortcode\" data-id=\"83abc62\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">When a function admits a finite limit <span class=\"katex-eq\" data-katex-display=\"false\">l \\in \\mathbb{R}<\/span> when <span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\infty<\/span>, then we say that <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> admits a hor<izontal asymptote of equation [latex]y = l[\/latex]. In other words, the curve moves closer and closer to the straight line [latex]y=l[\/latex].\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5a295e0 elementor-widget elementor-widget-heading\" data-id=\"5a295e0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">- Infinite limits at a finite value<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cdbb262 elementor-widget elementor-widget-shortcode\" data-id=\"cdbb262\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{|c|c|} \n\t\\hline \\text{Function} &amp; \\text{Limit} 0, \\: x \\to 0 \\\\\n\t\\hline f(x) = \\frac{1}{x}  &amp; \\begin{cases} &amp; +\\infty \\text{ si } x \\gt 0 \\\\ &amp; \\infty \\text{ si } x \\lt 0 \\end{cases} \\\\\n\t\\hline nan &amp; nan \\\\\n\t\\hline f(x) = \\ln(x) &amp; -\\infty  \\\\\n\t\\hline f(x) = \\sqrt{x} &amp; 0 \\\\\n\t\\hline\n\\end{array}\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ab11dc7 elementor-widget elementor-widget-shortcode\" data-id=\"ab11dc7\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">When <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to a} f(x) = \\pm \\infty<\/span>, with <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> a real number, then the curve of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> is said to have a vertical asymptote at <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>. In other words, the curve moves closer and closer to the straight line with equation <span class=\"katex-eq\" data-katex-display=\"false\">x=a<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-553fc46 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"553fc46\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Find out more about our Data Science training courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ec426a6 e-flex e-con-boxed e-con\" data-id=\"ec426a6\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-07670ca elementor-widget elementor-widget-heading\" data-id=\"07670ca\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Limit operations<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ecf2c60 elementor-widget elementor-widget-shortcode\" data-id=\"ecf2c60\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">In most cases, it is possible to perform limit operations to determine the limit.<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e1e0581 elementor-widget elementor-widget-shortcode\" data-id=\"e1e0581\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Limit of a sum of two functions<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15a56a3 elementor-widget elementor-widget-image\" data-id=\"15a56a3\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Limite-Somme.png\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"Jam AWS: The playful learning platform from Amazon\" data-elementor-lightbox-description=\"&lt;h2&gt;Jam AWS is a social, fun, and competitive learning platform for the Amazon Web Services Cloud and its various services for DevOps, Machine Learning, Cybersecurity, Networking, and more. Learn everything you need to know here: history, presentation, benefits, prerequisites, training and much more.&lt;\/h2&gt;\nIn 2018, &lt;a href=&quot;https:\/\/aws.amazon.com\/de\/&quot; target=&quot;_blank&quot; rel=&quot;noopener&quot;&gt;Amazon Web Services&lt;\/a&gt; saw an increase in demand for hands-on training on its cloud services. Users of the platform were looking for ways to familiarize themselves with &lt;a href=&quot;https:\/\/datascientest.com\/de\/amazon-web-service-aws-microsoft-azure-oder-google-cloud-platform-gcp&quot; target=&quot;_blank&quot; rel=&quot;noopener&quot;&gt;AWS&lt;\/a&gt; through real-world scenarios.\nTo meet this need, the cloud giant began developing an online training program that would allow users to practice using AWS in an enterprise-like environment without having to invest in expensive hardware.\n\nThus was born &lt;strong&gt;Jam AWS&lt;\/strong&gt;: an initiative to help users gain cloud skills through practice while having fun.\n&lt;h3&gt;What is Jam AWS?&lt;\/h3&gt;\nJam AWS is an &lt;strong&gt;online learning platform&lt;\/strong&gt; developed by Amazon Web Services to give users the opportunity to learn and practice about the various &lt;strong&gt;cloud services&lt;\/strong&gt;.\n\nThis hands-on experience allows users to work on real and concrete scenarios in a virtual environment similar to that of a company. It is also a social learning platform where users can &lt;strong&gt;interact with other learners&lt;\/strong&gt; and share their experiences.\nIn addition, participants can earn badges and rewards based on their performance. By improving one&#039;s score, it is possible to move up in the leaderboard. This adds a game-like dimension that makes the experience engaging and motivating.\n\nAmazon Jams are immersive experiences designed to give participants the opportunity to &lt;strong&gt;expand their knowledge&lt;\/strong&gt; of the AWS cloud and partner services. They consist of using the cloud services to complete challenges &lt;strong&gt;inspired by real-world scenarios&lt;\/strong&gt;.\n\nThrough these challenges, participants can identify their &lt;strong&gt;strengths&lt;\/strong&gt; and &lt;strong&gt;weaknesses&lt;\/strong&gt; and find out where they can improve. It&#039;s also an opportunity to learn how to collaborate in the cloud by overcoming challenges as a team. So this is a great opportunity to learn how to work with AWS.\n\nThe different experiences cover a wide variety of AWS services, through a range of scenarios prepared for common operational tasks and use cases. &lt;strong&gt;These include automation, cybersecurity incident response, artificial intelligence and machine learning, DevOps, or networking.&lt;\/strong&gt;\n\n&lt;a href=&quot;https:\/\/datascientest.com\/en\/aws-training&quot;&gt;\nGet to know the training\n&lt;\/a&gt;\n&lt;h3&gt;What are the advantages and benefits of Jam AWS?&lt;\/h3&gt;\nJam AWS brings several benefits to participants. First of all, it&#039;s an opportunity to master the different AWS services while having fun, thanks to fun challenges that you can do alone or in a team.\nYou can learn and discover at your own pace, freely taking in the different tools offered on the cloud platform. You can work on &lt;strong&gt;realistic challenges&lt;\/strong&gt; in a &lt;strong&gt;virtual environment&lt;\/strong&gt; similar to that of a company.\n\nWhen you sign up for these events, you&#039;ll have the opportunity to learn best practices from &lt;strong&gt;AWS experts&lt;\/strong&gt;. This is an opportunity to get hands-on experience and understand how to use Amazon&#039;s cloud services to solve various problems.\n\nThis online learning platform can be accessed from any internet-enabled device and therefore offers &lt;strong&gt;great flexibility&lt;\/strong&gt;. A wide variety of challenges are offered, covering many areas from &lt;strong&gt;application&lt;\/strong&gt; &lt;strong&gt;development&lt;\/strong&gt; to &lt;strong&gt;cybersecurity&lt;\/strong&gt; to &lt;strong&gt;data&lt;\/strong&gt; &lt;strong&gt;science&lt;\/strong&gt;.\nUsers can interact with other learners and share their experiences. This helps create a &lt;strong&gt;dynamic&lt;\/strong&gt; and &lt;strong&gt;social&lt;\/strong&gt; &lt;strong&gt;learning&lt;\/strong&gt; &lt;strong&gt;community&lt;\/strong&gt;.\nFinally, real-time leaderboards provide a way to track your progress. A scoring system allows you to measure your performance concretely, alongside other metrics such as the time spent on each challenge.\nIt also automatically scores the approach you use based on established best practices. This allows you to improve with each attempt.\n&lt;h3&gt;The different Jam AWS&lt;\/h3&gt;\nThere are two main categories of Jam AWS: &lt;strong&gt;team challenges and individual challenges&lt;\/strong&gt;. Each has its own unique characteristics.\n\n&lt;strong&gt;Team jams&lt;\/strong&gt; involve working together in a &lt;strong&gt;4- to 8-hour competition&lt;\/strong&gt; on a specific topic or over several days at events such as AWS Summits.\nUsing score tables and time pressure, these team challenges provide a &lt;strong&gt;fun and competitive learning experience&lt;\/strong&gt;.\n&lt;strong&gt;Individual jams&lt;\/strong&gt; allow you to progress at your own pace. You can take these challenges at your leisure to develop your skills and learn more about a technology topic.\nThis approach provides &lt;strong&gt;flexibility&lt;\/strong&gt; in scheduling challenges and allows students to independently track their own progress and skill level.\n\nIn both cases, participation is entirely remote via the Internet. &lt;strong&gt;Instant messaging, video conferencing, audio chat, and screen sharing&lt;\/strong&gt; can be used to collaborate or enlist the help of Amazon employees.\n&lt;h3&gt;How does a JAM AWS session work?&lt;\/h3&gt;\nFirst, the user must choose from a series of &lt;strong&gt;online training sessions&lt;\/strong&gt; offered on the Jam AWS Jam platform. Each of these sessions focuses on a specific topic related to &lt;a href=&quot;https:\/\/datascientest.com\/en\/cloud-computing-all-about&quot; target=&quot;_blank&quot; rel=&quot;noopener&quot;&gt;cloud computing&lt;\/a&gt; or application development.\nOnce the participant has made their choice, they are given access to a virtual lab where they can work on hands-on scenarios. This is an &lt;strong&gt;AWS platform&lt;\/strong&gt; configured specifically for the learning session.\n\nThe user then works on &lt;strong&gt;practical challenges&lt;\/strong&gt; that enable them to apply the concepts presented in the training session. These challenges are designed to help gain hands-on experience with AWS services.\nWhen necessary, people can access &lt;strong&gt;real-time technical support&lt;\/strong&gt; to get answers to their questions or get help solving problems. Users can also interact with other learners to share their experiences or ask questions.\n\nDepending on their performance in the hands-on challenges, users can earn badges and rewards and receive a score. This is an added incentive to excel and improve one&#039;s level.\n\n&lt;img width=&quot;640&quot; height=&quot;366&quot; src=&quot;https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2023\/08\/aws-jam2.png&quot; alt=&quot;A man and a woman are sitting in front of a laptop&quot; loading=&quot;lazy&quot; srcset=&quot;https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2023\/08\/aws-jam2.png 640w, https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2023\/08\/aws-jam2-300x172.png 300w&quot; sizes=&quot;(max-width: 640px) 100vw, 640px&quot;&gt;\n&lt;a href=&quot;https:\/\/www.youtube.com\/watch?v=LFGMNpGTjQk&quot; target=&quot;_blank&quot; rel=&quot;noopener&quot;&gt;\nAWS kennenlernen\n&lt;\/a&gt;\n&lt;h3&gt;How can I participate in an AWS Jam?&lt;\/h3&gt;\nJam AWS challenges can be customized according to experience level and are therefore suitable for both &lt;strong&gt;novices&lt;\/strong&gt; and seasoned &lt;strong&gt;professionals&lt;\/strong&gt;. Different difficulty levels are offered: &lt;strong&gt;easy, medium, and hard&lt;\/strong&gt;.\n\nThis learning platform is aimed at developers, architects, cybersecurity experts, machine learning experts, and, of course, cloud professionals. Different professionals can collaborate to find the optimal solutions to a specific challenge.\nTo participate, the first step is to &lt;strong&gt;create an AWS account&lt;\/strong&gt;. This is a requirement to access the Amazon Web Services console and virtual lab.\nIt is important to know the basic AWS services and how they work. You can consult the official documentation or sign up for a course like the one &lt;strong&gt;offered by DataScientest&lt;\/strong&gt;.\nDepending on the topic you choose, you&#039;ll need to take AWS courses on architecture, development, DevOps engineering, cybersecurity, or cloud operations.\n\nA computer and internet connection are essential. Make sure your computer is compatible with the technical requirements of the course. Also, if it&#039;s a team jam, make sure you have enough free time to participate and take on the challenge!\n&lt;h3&gt;Conclusion: AWS Jam, an ideal way to learn the cloud through practice.&lt;\/h3&gt;\nSince its launch, AWS Jam has been a huge hit with users of the cloud platform. These challenges provide a hands-on and interactive way to learn skills.\nThe offering has expanded over time and now provides training sessions and hands-on challenges that allow you to become a true expert on the various cloud services.\nToday, AWS Jam continues to improve to meet the ever-changing needs of Amazon Web Services users. It is a &lt;strong&gt;great social learning platform&lt;\/strong&gt; to advance your career in the cloud.\n\nTo learn how to master AWS and its various services, you can also choose DataScientest and its four-day online training course. With this program, you can prepare for an &lt;strong&gt;official Amazon Web Services certification&lt;\/strong&gt;.\nYou&#039;ll learn how to use AWS services to make your &lt;strong&gt;infrastructure&lt;\/strong&gt; &lt;strong&gt;scalable&lt;\/strong&gt;, how to identify procedures for migrating to the cloud, and how to design solutions that include &lt;strong&gt;security&lt;\/strong&gt;, &lt;strong&gt;authentication&lt;\/strong&gt;, and &lt;strong&gt;access&lt;\/strong&gt; &lt;strong&gt;features&lt;\/strong&gt;.\nIn this course, you&#039;ll learn about the AWS cloud and its fundamental concepts and architectures, and how to design, improve, and automate network architectures.\n\nBy the end of the course, you will be able to set up a cloud project, develop applications from within AWS, design resilient and secure architectures, and automate tasks. These skills are in &lt;strong&gt;high demand in companies&lt;\/strong&gt;!\n\nOur organization has the title of an &lt;strong&gt;official Amazon Training Partner&lt;\/strong&gt; and all of our courses are taught by instructors who are certified as &lt;strong&gt;Amazon Authorized Instructors&lt;\/strong&gt;. Discover DataScientest fast!\n\n&lt;a href=&quot;https:\/\/datascientest.com\/en\/aws-training&quot; target=&quot;_blank&quot; rel=&quot;noopener&quot;&gt;\nMore information about the AWS training\n&lt;\/a&gt;\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTY5Nzc4LCJ1cmwiOmZhbHNlfQ%3D%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Limite-Somme.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f505b00 elementor-widget elementor-widget-shortcode\" data-id=\"f505b00\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Limit of a product of two functions<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5fe7417 elementor-widget elementor-widget-image\" data-id=\"5fe7417\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Capture-de\u0301cran-2022-07-28-a\u0300-14.40.34.png\" data-elementor-open-lightbox=\"yes\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTY5NzgzLCJ1cmwiOmZhbHNlfQ%3D%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Capture-de\u0301cran-2022-07-28-a\u0300-14.40.34.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-74b959b elementor-widget elementor-widget-shortcode\" data-id=\"74b959b\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Limit of a quotient of two functions<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49b6acc elementor-widget elementor-widget-image\" data-id=\"49b6acc\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Limite-quotien.png\" data-elementor-open-lightbox=\"yes\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTY5Nzg0LCJ1cmwiOmZhbHNlfQ%3D%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/07\/Limite-quotien.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9118d95 elementor-widget elementor-widget-heading\" data-id=\"9118d95\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<span class=\"elementor-heading-title elementor-size-default\">Click on the tables to display them full-screen.<\/span>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8b3a6d5 e-flex e-con-boxed e-con\" data-id=\"8b3a6d5\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-817a7f2 elementor-widget elementor-widget-heading\" data-id=\"817a7f2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Determining a limit in practice\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e26fd87 elementor-widget elementor-widget-shortcode\" data-id=\"e26fd87\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">To determine limits, it's sometimes simpler to use other functions. <br>\nComparing functions allows you to compare their limits, when they exist.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-87866dc elementor-widget elementor-widget-shortcode\" data-id=\"87866dc\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">There are two main properties for comparing functions\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8564cfc elementor-widget elementor-widget-heading\" data-id=\"8564cfc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">- Comparison theorem\n<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-964b5f2 elementor-widget elementor-widget-shortcode\" data-id=\"964b5f2\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Let <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> be two functions defined on an interval <span class=\"katex-eq\" data-katex-display=\"false\">I = [a, +\\infty[<\/span>. <br>\nAssume that for any <span class=\"katex-eq\" data-katex-display=\"false\">x \\in I ; f(x) \\geq g(x)<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-62ef90e elementor-widget elementor-widget-shortcode\" data-id=\"62ef90e\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">If <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to +\\infty}g(x) = +\\infty<\/span>, so <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to +\\infty}f(x) = +\\infty<\/span>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8a4925 elementor-widget elementor-widget-shortcode\" data-id=\"d8a4925\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">If <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to +\\infty}f(x) = -\\infty<\/span>, so <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to +\\infty}g(x) = -\\infty<\/span>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7bcf498 elementor-widget elementor-widget-heading\" data-id=\"7bcf498\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">- Gendarme theorem<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fd0b4eb elementor-widget elementor-widget-shortcode\" data-id=\"fd0b4eb\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Let <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> be three functions <defined on an interval [latex]I = [a, +\\infty[[\/latex]]. <br>\nAssume that for any <span class=\"katex-eq\" data-katex-display=\"false\">x \\in I ; g(x) \\leq f(x) \\leq h(x)<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a8ce7f elementor-widget elementor-widget-shortcode\" data-id=\"7a8ce7f\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">If <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> tend to the same limit <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> in <span class=\"katex-eq\" data-katex-display=\"false\">+\\infty<\/span>, then <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to +\\infty}g(x) = +\\infty<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3f39777 elementor-widget elementor-widget-shortcode\" data-id=\"3f39777\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">You now know what a limit is and how to calculate it. Calculating limits allows you, for example, to define the derivative of a function as the limit of a rate of increase. <\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ba9ff5f elementor-widget elementor-widget-shortcode\" data-id=\"ba9ff5f\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">If you'd like to discover all the mathematical concepts involved in data science, we invite you to take a look at our curricula.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b90b83 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"9b90b83\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Training in Data Science<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>All scientific disciplines are based on mathematics, and data science is no exception. When the problems to be solved are optimization problems, you need to know what the limit of a function is. In this article, you&#8217;ll discover how to determine the limit of a function. Limit: Definition The limit of a function is the [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":178043,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Limit of a function: how to determine it?<\/title>\n<meta name=\"description\" content=\"All scientific disciplines are based on mathematics, and data science is no exception. 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