{"id":887,"date":"2025-06-20T17:20:02","date_gmt":"2025-06-20T17:20:02","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/?post_type=chapter&#038;p=887"},"modified":"2025-10-10T04:08:52","modified_gmt":"2025-10-10T04:08:52","slug":"separation-of-variables-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/separation-of-variables-apply-it-2\/","title":{"raw":"The Divergence and Integral Tests: Apply It","rendered":"The Divergence and Integral Tests: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Use the divergence test to check if a series might converge<\/li>\r\n \t<li>Apply the integral test to determine if a series converges<\/li>\r\n \t<li>Estimate how close a partial sum is to the actual sum of a series<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Battery Life Analysis<\/h2>\r\n<p class=\"whitespace-normal break-words\">Modern smartphones rely on efficient power management to maximize battery life. Battery consumption follows predictable patterns that can be modeled mathematically. As a tech support specialist, you need to analyze battery drain rates to help customers optimize their device performance and determine when batteries need replacement.<\/p>\r\n<p class=\"whitespace-normal break-words\">Consider a smartphone where the battery drain rate (measured in percentage per hour) follows the function [latex]f(t) = \\frac{1}{t^{1.5}}[\/latex], where [latex]t[\/latex] represents hours since the phone was taken off the charger. This model accounts for how battery drain typically decreases over time as background processes optimize and the screen dims.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313485[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313486[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313487[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313488[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313489[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Use the divergence test to check if a series might converge<\/li>\n<li>Apply the integral test to determine if a series converges<\/li>\n<li>Estimate how close a partial sum is to the actual sum of a series<\/li>\n<\/ul>\n<\/section>\n<h2>Battery Life Analysis<\/h2>\n<p class=\"whitespace-normal break-words\">Modern smartphones rely on efficient power management to maximize battery life. Battery consumption follows predictable patterns that can be modeled mathematically. As a tech support specialist, you need to analyze battery drain rates to help customers optimize their device performance and determine when batteries need replacement.<\/p>\n<p class=\"whitespace-normal break-words\">Consider a smartphone where the battery drain rate (measured in percentage per hour) follows the function [latex]f(t) = \\frac{1}{t^{1.5}}[\/latex], where [latex]t[\/latex] represents hours since the phone was taken off the charger. This model accounts for how battery drain typically decreases over time as background processes optimize and the screen dims.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313485\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313485&theme=lumen&iframe_resize_id=ohm313485&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313486\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313486&theme=lumen&iframe_resize_id=ohm313486&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313487\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313487&theme=lumen&iframe_resize_id=ohm313487&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313488\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313488&theme=lumen&iframe_resize_id=ohm313488&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313489\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313489&theme=lumen&iframe_resize_id=ohm313489&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":671,"module-header":"- Select Header -","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\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/887"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":9,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/887\/revisions"}],"predecessor-version":[{"id":2378,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/887\/revisions\/2378"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/671"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/887\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=887"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=887"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=887"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}