{"id":496,"date":"2025-02-13T19:45:28","date_gmt":"2025-02-13T19:45:28","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/calculus-of-the-hyperbolic-functions-apply-it\/"},"modified":"2025-02-13T19:45:28","modified_gmt":"2025-02-13T19:45:28","slug":"calculus-of-the-hyperbolic-functions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/calculus-of-the-hyperbolic-functions-apply-it\/","title":{"raw":"Calculus of the Hyperbolic Functions: Apply It","rendered":"Calculus of the Hyperbolic Functions: Apply It"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Differentiate and integrate hyperbolic functions and their inverse forms<\/li>\n\t<li>Understand the practical situations where the catenary curve appears<\/li>\n<\/ul>\n<\/section>\n<h2>Calculus of the Hyperbolic Functions<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/uMXcKY_w3w4?si=tZS9Vk1wwHJVR3jn\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/Q6-QZxUDfE0?si=ADF7DbLDS7kVAkx2\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">Pause these videos at the beginning and try to solve the problems on your own. Then, resume watching the video to check if you solved them correctly.<br>\n<br>\n<iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/u-_J0KjG1PU?si=M40Np8g021pntjMm\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/dmAf1dUQNl8?si=LEtxZGstgiygWOwR\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/AlQAOmL14Uw?si=6ZhsogYxpL0UBdxQ\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/S58WptODiZ4?si=DkQKTdfCo-hdhGJ7\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/V4Atg5NbHOw?si=KrKHZsxH_kyrBobV\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/I9MV2FLxkIE?si=4UkYsroQU8923YSR\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<p>&nbsp;<\/p>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Differentiate and integrate hyperbolic functions and their inverse forms<\/li>\n<li>Understand the practical situations where the catenary curve appears<\/li>\n<\/ul>\n<\/section>\n<h2>Calculus of the Hyperbolic Functions<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/uMXcKY_w3w4?si=tZS9Vk1wwHJVR3jn\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/Q6-QZxUDfE0?si=ADF7DbLDS7kVAkx2\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">Pause these videos at the beginning and try to solve the problems on your own. Then, resume watching the video to check if you solved them correctly.<\/p>\n<p><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/u-_J0KjG1PU?si=M40Np8g021pntjMm\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/dmAf1dUQNl8?si=LEtxZGstgiygWOwR\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/AlQAOmL14Uw?si=6ZhsogYxpL0UBdxQ\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/S58WptODiZ4?si=DkQKTdfCo-hdhGJ7\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/V4Atg5NbHOw?si=KrKHZsxH_kyrBobV\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe> <iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/I9MV2FLxkIE?si=4UkYsroQU8923YSR\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<p>&nbsp;<\/p>\n","protected":false},"author":6,"menu_order":17,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":479,"module-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\/496"}],"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\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/496\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/479"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/496\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=496"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=496"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=496"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}