{"version":"1.0","provider_name":"eTrapez Online","provider_url":"https:\/\/online.etrapez.pl\/en\/","author_name":"Krystian Karczy\u0144ski","author_url":"https:\/\/blog.etrapez.pl\/o-nas\/#krystian-karczynski","title":"Limits Course - eTrapez Online","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"3ByUOPxfDs\"><a href=\"https:\/\/online.etrapez.pl\/en\/course\/limits-course\/\">Limits Course<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/online.etrapez.pl\/en\/course\/limits-course\/embed\/#?secret=3ByUOPxfDs\" width=\"600\" height=\"338\" title=\"&#8220;Limits Course&#8221; &#8212; eTrapez Online\" data-secret=\"3ByUOPxfDs\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script>\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/\/# sourceURL=https:\/\/online.etrapez.pl\/wp-includes\/js\/wp-embed.min.js\n<\/script>\n","thumbnail_url":"https:\/\/online.etrapez.pl\/wp-content\/uploads\/sites\/2\/2015\/08\/granice-eng-beztla.png","thumbnail_width":1024,"thumbnail_height":674,"description":"The Limits Course is a multimedia educational program divided into eight themed lessons. The first lesson introduces the calculation of limits, while the final lesson covers the continuity of functions. The course offers around 350 minutes of video in which I explain\u2014slowly and from first principles\u2014and demonstrate how to solve each problem. The videos come with 80 knowledge-check quiz questions and roughly 120 hand-picked practice exercises. In this course, I share the expertise I have accumulated over many years of intensively teaching limits to students at a variety of universities. From it you will learn, among other things:  How to grasp, in a straightforward way, what the limits of sequences are\u2014and why that insight is so helpful when you need to compute them. What are the two basic, elementary limit formulas\u2014used at practically every step\u2014that many beginners don\u2019t even realize exist when they first start studying How to effortlessly distinguish between the two versions of limits\u2014the easier and the harder cases\u2014when using multiplication by the conjugate. Where did the number e come from in mathematics? Which high-school facts about sequences you really don\u2019t need \u2014 and there are quite a lot of them. Why the seemingly simplest limit problems for functions can in fact be the toughest\u2014and how to guard against that. About the many simple tricks that steer you toward the right limit formulas for functions. When a function\u2019s limit does not exist\u2014and what a struggling student can do about it. That continuity problems are generally the easiest limit problems\u2014and why. \u2026and many, many other practical, battle-tested \u201ctricks\u201d that, in addition to a solid, almost six-hour dose of foundational knowledge, may let you astonish\u2014even yourself\u2014during a limits quiz or exam."}