{"id":31743,"date":"2022-09-21T15:27:00","date_gmt":"2022-09-21T07:27:00","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=31743"},"modified":"2026-03-09T14:43:08","modified_gmt":"2026-03-09T06:43:08","slug":"ca022_2-6","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-103%e5%ad%b8%e5%b9%b4%e5%ba%a6-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e8%8e%8a%e9%87%8d%e8%80%81%e5%b8%ab\/ca022_2-6","title":{"rendered":"2.6 Limits at Infinity, Horizontal Asymptotes"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"31743\" class=\"elementor elementor-31743\">\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-16700d17 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-6ad968e6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ad968e6\" 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-52987d63\" data-id=\"52987d63\" 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-e5808cb elementor-widget elementor-widget-heading\" data-id=\"e5808cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">2.6 Limits at Infinity, Horizontal Asymptotes\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element 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class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-652aa46c elementor-widget elementor-widget-penci-button\" data-id=\"652aa46c\" data-element_type=\"widget\" data-widget_type=\"penci-button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pcbtn-wrapper pcbtn-align-left\">\r\n\t\t\t<a class=\"pcbtn pcbtn-icon-left elementor-animation-grow\" href=\"\/?post_type=course_page&#038;p=29260\">\r\n\t\t\t\t<span class=\"pcbtn-wrapperin\">\r\n\t\t\t\t\t<span class=\"pcbtn-content\"><svg class=\"e-font-icon-svg e-fas-arrow-left\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M257.5 445.1l-22.2 22.2c-9.4 9.4-24.6 9.4-33.9 0L7 273c-9.4-9.4-9.4-24.6 0-33.9L201.4 44.7c9.4-9.4 24.6-9.4 33.9 0l22.2 22.2c9.5 9.5 9.3 25-.4 34.3L136.6 216H424c13.3 0 24 10.7 24 24v32c0 13.3-10.7 24-24 24H136.6l120.5 114.8c9.8 9.3 10 24.8.4 34.3z\"><\/path><\/svg>\u8fd4\u56de\u8ab2\u7a0b\u9996\u9801<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/span>\r\n\t\t\t<\/a>\r\n\t\t<\/div>\r\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-2 penci-sticky-ct    elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-fc8fc3b\" data-id=\"fc8fc3b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\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<div class=\"elementor-element elementor-element-546b36ef elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"546b36ef\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 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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-da19150 elementor-widget elementor-widget-shortcode\" data-id=\"da19150\" 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-62\" class=\"tablepress tablepress-id-62\">\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\">\u838a\u91cd\u8001\u5e2b\u771f\u5fc3\u544a\u767d<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=29309\">\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\">\u8ab2\u7a0b\u4ecb\u7d39<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31711\">\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\">\u7b2c\u4e00\u7ae0 Functions and Models<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=31717\">\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\">\u7b2c\u4e8c\u7ae0 Limits and derivatives <br \/>\n2.2 The Limit of a Function <br \/>\n2.3 Calculating Limits Using the Limit Laws<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31723\">\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\">2.4 The Precise Definition of a Limit<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31731\">\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\">2.5 Continuity<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31737\">\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\">2.6 Limits at Infinity, Horizontal Asymptotes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31743\">\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\">2.7 Derivatives and Rates of Change<br \/>\n(\u672c\u5f71\u7247\u5167\u5bb9\u6709\u90e8\u5206\u932f\u8aa4\uff0c\u8a73\u898bYouTube\u7559\u8a00)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31749\">\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\">2.8 The Derivative as a Function<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31755\">\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\">\u7b2c\u4e09\u7ae0 Differentiation Rules<br \/>\n3.1 Derivatives of Polynomials and Exponential Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31761\">\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\">3.2 The Product and Quotient Rules<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31767\">\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\">3.3 Derivatives of Trigonometric Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31773\">\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\">3.4 The Chain Rule<br \/>\n(\u672c\u5f71\u7247\u5167\u5bb9\u6709\u90e8\u5206\u932f\u8aa4\uff0c\u8a73\u898bYouTube\u7559\u8a00) <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31779\">\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\">3.5 Implicit Differentiation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31787\">\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\">3.6 Derivatives of Logarithmic Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31793\">\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\">3.9 Related Rates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31799\">\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\">3.10 Linear Approximations and Differentials<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31805\">\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\">\u7b2c\u56db\u7ae0 Applications of Differentiation<br \/>\n4.1 Maximum and Minimum Values <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31811\">\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\">4.2 The Mean Value Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31819\">\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\">4.3 How Derivatives Affect the Shape of a Graph<br \/>\n4.5 Summary of Curve Sketching<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31825\">\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\">4.4 Indeterminate Forms and L\u2019Hospital\u2019s Rule<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31831\">\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\">4.7 Optimization Problems<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31837\">\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\">4.9 Antiderivatives<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31843\">\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\">\u7b2c\u4e94\u7ae0 Integrals<br \/>\n 5.1 Areas and Distances <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31849\">\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\">5.2 The Definite Integral<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31855\">\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\">5.3 The Fundamental Theorem of Calculus<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31861\">\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\">5.4 Indefinite Integrals and the Net Change Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31867\">\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\">5.5 The Substitution Rule<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31873\">\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\">\u7b2c\u516d\u7ae0 Applications of Integration <br \/>\n6.1 Areas between Curves <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31879\">\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\">6.2 Volumes<br \/>\n6.3 Volumes by Cylindrical Shells<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31885\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">6.5 Average Value of a Function<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31891\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e03\u7ae0 Techniques of Integration <br \/>\n7.1 Integration by Parts<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31897\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-34 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.2 Trigonometric Integrals<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31903\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-35 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.3 Trigonometric Substitution<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31909\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-36 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.4 Integration of Rational Functions by Partial Fractions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31915\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-37 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.7 Approximate Integration<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31928\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-38 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=31934\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-39 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 Further Applications of Integration<br \/>\n8.1 Arc Length<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31940\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-40 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8.2 Area of a Surface of Revolution<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31946\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-41 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8.5 Probability<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31952\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-42 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u5341\u7ae0 Parametric Equations and Polar Coordinates<br \/>\n10.1 Curves Defined by Parametric Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31958\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-43 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10.2 Calculus with Parametric Curves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=31964\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-62 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-5f099062\" data-id=\"5f099062\" 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-5b79cc32 elementor-widget-divider--view-line_text elementor-widget-divider--element-align-center 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