{"id":14742,"date":"2022-08-15T17:12:17","date_gmt":"2022-08-15T09:12:17","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=14742"},"modified":"2026-03-23T11:28:08","modified_gmt":"2026-03-23T03:28:08","slug":"ca961_961029","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e5%be%ae%e7%a9%8d%e5%88%86%e4%b8%80-calculus-i-english-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e7%ac%a6%e9%ba%a5%e5%85%8b%e8%80%81%e5%b8%ab\/ca961_961029","title":{"rendered":"4-4 Indeterminate Forms a nd L\u2019Hospital\u2019s Rule"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"14742\" class=\"elementor elementor-14742\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-27f425e5 elementor-section-boxed elementor-section-height-default 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href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-43d3b5df elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"43d3b5df\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-2e31d00\" data-id=\"2e31d00\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-62afa6e2 elementor-widget elementor-widget-penci-info-box\" data-id=\"62afa6e2\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_61952\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t\t\t\t\t\t<h3 class=\"penci-ibox-title\">4-4 Indeterminate Forms a nd L\u2019Hospital\u2019s Rule\n<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53f374c4 elementor-widget elementor-widget-video\" data-id=\"53f374c4\" data-element_type=\"widget\" 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100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73059f3c elementor-widget elementor-widget-shortcode\" data-id=\"73059f3c\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">\n<table id=\"tablepress-23\" class=\"tablepress tablepress-id-23\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter1 Functions and Model<br \/>\n1-5 Exponential Functions  <br \/>\n1-6 Inverse Functions and Logarithms<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14665\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter2 Limits and Derivatives<br \/>\n2-2 The Limit of a Function <br \/>\n2-4 The Precise Definition of a Limit<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14676\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2-3 Calculating Limits Using the Limit Laws<br \/>\n2-6 Limits at Infinity: Horizontal Asymptotes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14682\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2-5 Continuity<br \/>\n2-6 Limits at Infinity; Horizontal Asymptotes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14688\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2-8 Derivatives <br \/>\n2-9 The Derivative as a Function<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14694\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter3 Differentiation Rules<br \/>\n3-1 Derivatives of Polynomials and Exponential Functions <br \/>\n3-2 The Product and Quotient Rules <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14700\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3-4 Derivatives of Trigonometric Functions<br \/>\n3-5 The Chain Rule<br \/>\n3-6 Implicit Differentiation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14706\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3-6 Implicit Differentiation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14712\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3-8 Derivatives of Logarithmic Functions<br \/>\n3-10 Related Rates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14718\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3-7 Higher Derivatives <br \/>\n3-11 Linear Approximations and Differentials<br \/>\nChapter4 Applications of Differation<br \/>\n4-1 Maximum and Minimum Values<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14724\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4-1 Maximum and Minimum Values<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14730\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4-2 The Mean Value Theorem<br \/>\n4-3 How Derivatives Affect the Shape of a Graph<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14736\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4-4 Indeterminate Forms a nd L\u2019Hospital\u2019s Rule<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14742\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4-7 Optimization Problems<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14748\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4-5 Summary of Curve Sketching<br \/>\n4-7 Optimization Problems<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14754\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4-7 Optimization Problems<br \/>\n4-10 Antiderivatives<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14760\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter5 Integrals<br \/>\n5-1 Areas and Distances <br \/>\n5-2 The Definite Integral<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14770\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">5-2 The Definite Integral<br \/>\n5-3 The Fundamental Theorem of Calculus<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14776\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">5-4 Indefinite Integrals and the Total Change Theorem<br \/>\n5-5 The Substitution Rule<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14782\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">5-5 The Substitution Rule  <br \/>\n5-6 The Logarithm Defined as an Integral<br \/>\nChapter6 Applications of Integration<br \/>\n6-1 Areas between Curves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14788\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">6-1 Areas between Curves <br \/>\n6-2 Volumes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14794\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">6-3 Volumes be Cylindrical Shells<br \/>\nChapter7 Techniques of Integration<br \/>\n7-1 Integration by Parts <br \/>\n7-2 Trigonometric Integrals<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14800\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7-2 Trigonometric Integrals<br \/>\n7-3 Trigonometric Substitution<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14806\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7-4 Integration of Rational Functions by Partial Fractions <br \/>\n7-8 Improper Integrals<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14812\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7-8 Improper Integrals<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14818\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7-7 Approximate Integration <br \/>\nChapter8 Further Applications of Integration<br \/>\n8-1 Arc Length<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14830\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8-1 Arc Length <br \/>\n8-2 Area of a Surface of Revolution<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14836\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter10 Parametric Equations and Polar Coordinates<br \/>\n10-1 Curves Defined by Parametric Equations <br \/>\n10-2 Calculus with Parametric Curves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14842\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10-2 Calculus with Parametric Curves  <br \/>\n10-3 Polar Coordinates <br \/>\n10-4 Areas and Lengths in Polar Coordinates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14848\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10-3 Polar Coordinates<br \/>\n10-4 Areas and Lengths in Polar Coordinates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=14854\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-23 from cache --><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-3 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-48a0b44\" data-id=\"48a0b44\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-62a7c21 elementor-widget-divider--view-line_text elementor-widget-divider--element-align-center elementor-widget 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