{"id":3404,"date":"2024-06-24T16:28:54","date_gmt":"2024-06-24T16:28:54","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3404"},"modified":"2024-08-05T12:20:01","modified_gmt":"2024-08-05T12:20:01","slug":"a-preview-of-calculus-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/a-preview-of-calculus-apply-it\/","title":{"raw":"A Preview of Calculus: Apply It","rendered":"A Preview of Calculus: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify the line that just touches a curve at one point by looking at how nearby lines approach it<\/li>\r\n\t<li>Describe how integration can be used to calculate the area under a curve<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Caitlin Clark, regarded as one of the greatest collegiate players of all time, joined the Indiana Fever of the Women's National Basketball Association in 2024. When she shoots a basketball, the height of the ball (in feet) [latex]t[\/latex] seconds after it leaves her hands is given by\u00a0<\/p>\r\n<p style=\"text-align: center;\">[latex]h(t)=-16t2+24t+8[\/latex]<\/p>\r\n<p>The ball arcs through the air and passes cleanly through the basket which is [latex]10[\/latex] feet above the ground. It\u2019s a swish!<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]287758[\/ohm_question]<\/p>\r\n<\/section>\r\n<p>Caitlin Clark is dealing with fractions of a second here! For the following exercises, complete any calculations with values rounded to five decimal places. 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