{"id":3441,"date":"2024-06-24T16:43:50","date_gmt":"2024-06-24T16:43:50","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3441"},"modified":"2024-08-13T14:13:28","modified_gmt":"2024-08-13T14:13:28","slug":"limits-at-infinity-and-asymptotes-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/limits-at-infinity-and-asymptotes-apply-it\/","title":{"raw":"Limits at Infinity and Asymptotes: Apply It","rendered":"Limits at Infinity and Asymptotes: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Determine limits and predict how functions behave as x increases or decreases indefinitely<\/li>\r\n\t<li>Identify and distinguish horizontal and slanting lines that a graph approaches but never touches<\/li>\r\n\t<li>Use a function\u2019s derivatives to accurately sketch its graph<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>From Party Planning to Paper Design: Exploring Function Behavior<\/h2>\r\n<p>In this apply-it task, we'll dive into the practical applications of function analysis in a business context. We'll explore two scenarios related to a company's employee party: determining the optimal attendance fee and designing the perfect invitation. These problems will challenge you to apply various calculus concepts, including domain analysis, limit evaluation, asymptote identification, and derivative calculations.<\/p>\r\n<p>By working through these problems, you'll gain insight into how calculus can be applied to make informed decisions in business planning and design. Let's begin our exploration of these real-world applications of function analysis!<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p><iframe id=\"ohm288058\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq2.php?id=288058&amp;theme=lumen&amp;iframe_resize_id=ohm288058&amp;source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p><iframe id=\"ohm288059\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq2.php?id=288059&theme=lumen&iframe_resize_id=ohm288059&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Determine limits and predict how functions behave as x increases or decreases indefinitely<\/li>\n<li>Identify and distinguish horizontal and slanting lines that a graph approaches but never touches<\/li>\n<li>Use a function\u2019s derivatives to accurately sketch its graph<\/li>\n<\/ul>\n<\/section>\n<h2>From Party Planning to Paper Design: Exploring Function Behavior<\/h2>\n<p>In this apply-it task, we&#8217;ll dive into the practical applications of function analysis in a business context. We&#8217;ll explore two scenarios related to a company&#8217;s employee party: determining the optimal attendance fee and designing the perfect invitation. These problems will challenge you to apply various calculus concepts, including domain analysis, limit evaluation, asymptote identification, and derivative calculations.<\/p>\n<p>By working through these problems, you&#8217;ll gain insight into how calculus can be applied to make informed decisions in business planning and design. Let&#8217;s begin our exploration of these real-world applications of function analysis!<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p><iframe loading=\"lazy\" id=\"ohm288058\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq2.php?id=288058&amp;theme=lumen&amp;iframe_resize_id=ohm288058&amp;source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p><iframe loading=\"lazy\" id=\"ohm288059\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq2.php?id=288059&#38;theme=lumen&#38;iframe_resize_id=ohm288059&#38;source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":292,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3441"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3441\/revisions"}],"predecessor-version":[{"id":4618,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3441\/revisions\/4618"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/292"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3441\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3441"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3441"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3441"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}