{"id":3045,"date":"2024-02-29T20:06:43","date_gmt":"2024-02-29T20:06:43","guid":{"rendered":"https:\/\/bezwarunku.pl\/?page_id=3045"},"modified":"2024-05-15T11:14:08","modified_gmt":"2024-05-15T10:14:08","slug":"regula-de-lhospitala","status":"publish","type":"page","link":"https:\/\/bezwarunku.pl\/index.php\/regula-de-lhospitala\/","title":{"rendered":"Regu\u0142a de l&#8217;Hospitala"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"3045\" class=\"elementor elementor-3045\" data-elementor-post-type=\"page\">\n\t\t\t\t<header class=\"elementor-element elementor-element-68c0e91 e-con-full e-flex e-con e-parent\" data-id=\"68c0e91\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-fec7d35 e-con-full e-flex e-con e-child\" data-id=\"fec7d35\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-32b3ff4 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600w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-100x100.jpg 100w\" sizes=\"(max-width: 1170px) 100vw, 1170px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c34ec41 e-con-full e-flex e-con e-child\" data-id=\"c34ec41\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-575b3d4 elementor-nav-menu--stretch elementor-widget__width-auto elementor-nav-menu__text-align-center elementor-nav-menu--dropdown-tablet elementor-nav-menu--toggle elementor-nav-menu--burger elementor-widget elementor-widget-nav-menu\" data-id=\"575b3d4\" data-element_type=\"widget\" data-settings=\"{&quot;full_width&quot;:&quot;stretch&quot;,&quot;layout&quot;:&quot;horizontal&quot;,&quot;submenu_icon&quot;:{&quot;value&quot;:&quot;&lt;svg class=\\&quot;e-font-icon-svg e-fas-caret-down\\&quot; viewBox=\\&quot;0 0 320 512\\&quot; 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tabindex=\"-1\">G\u0141\u00d3WNA<\/a><\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-177\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\" class=\"elementor-item\" tabindex=\"-1\">CENNIK<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4681\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/regulamin\/\" class=\"elementor-item\" tabindex=\"-1\">regulamin<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-167ab70 elementor-widget__width-auto elementor-widget elementor-widget-button\" data-id=\"167ab70\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/bezwarunku.pl\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">zarejestruj si\u0119<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/header>\n\t\t<div class=\"elementor-element elementor-element-dfec9a8 e-con-full e-flex e-con e-parent\" data-id=\"dfec9a8\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9f1a279 elementor-widget elementor-widget-heading\" data-id=\"9f1a279\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/analiza-matematyczna\/?preview_id=200&#038;preview_nonce=87c719741f&#038;preview=true\">POCHODNE<\/a><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-70413e6 animated-slow elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"70413e6\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInUp&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Regu\u0142a de l'Hospitala<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-48c4014 e-flex e-con-boxed e-con e-parent\" data-id=\"48c4014\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9dc1c85 elementor-widget elementor-widget-heading\" data-id=\"9dc1c85\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Je\u015bli licz\u0105c granic\u0119 funkcji \\(\\frac{f\\left(x\\right)}{g\\left(x\\right)}\\) wychodzi nam:  \\(\\frac00 lub\\;\\frac\\infty\\infty\\), to liczymy granic\u0119: \\(\\frac{f'\\left(x\\right)}{g'\\left(x\\right)}\\)<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-233f984 e-flex e-con-boxed e-con e-parent\" data-id=\"233f984\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-faa8a39 e-con-full e-flex e-con e-child\" data-id=\"faa8a39\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8904cab elementor-widget elementor-widget-toggle\" data-id=\"8904cab\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h4 id=\"elementor-tab-title-1431\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1431\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><svg class=\"elementor-toggle-icon-opened e-font-icon-svg e-fas-caret-up\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">KLIKNIJ TUTAJ<\/a>\n\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1431\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1431\"><p><img decoding=\"async\" class=\"size-full wp-image-3061 aligncenter\" src=\"http:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/wzory-pochodne-1.jpg\" alt=\"\" width=\"605\" height=\"440\" srcset=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/wzory-pochodne-1.jpg 605w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/wzory-pochodne-1-300x218.jpg 300w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/wzory-pochodne-1-600x436.jpg 600w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b60e598 elementor-widget elementor-widget-heading\" data-id=\"b60e598\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">WZORY:<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d7174b8 e-con-full e-flex e-con e-child\" data-id=\"d7174b8\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e58a14a elementor-widget elementor-widget-toggle\" data-id=\"e58a14a\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cd3ded elementor-widget elementor-widget-heading\" data-id=\"5cd3ded\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">1.Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow\\infty}\\frac{\\ln\\left(x\\right)}x$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6009ce1 e-con-full e-flex e-con e-child\" data-id=\"6009ce1\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ccd6167 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"ccd6167\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c77546 elementor-widget elementor-widget-heading\" data-id=\"9c77546\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">2.Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow\\infty}\\frac{e^x}x$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ad9743f e-con-full e-flex e-con e-child\" data-id=\"ad9743f\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-442e44e elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"442e44e\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d917ae6 elementor-widget elementor-widget-heading\" data-id=\"d917ae6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">3. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow0}\\frac{1-\\cos\\left(x\\right)}{\\sin\\left(x\\right)}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6ab3cfe e-con-full e-flex e-con e-child\" data-id=\"6ab3cfe\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8830a67 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"8830a67\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-70d1c72 elementor-widget elementor-widget-heading\" data-id=\"70d1c72\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">4. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow0}\\frac{5tg\\left(x\\right)}{\\sin\\left(5x\\right)}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0499abf e-con-full e-flex e-con e-child\" data-id=\"0499abf\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-103cb4c elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"103cb4c\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-43f84ea elementor-widget elementor-widget-heading\" data-id=\"43f84ea\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">5. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow0}\\frac{tg\\left(3x\\right)}{tg\\left(12x\\right)}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cb30e4a e-con-full e-flex e-con e-child\" data-id=\"cb30e4a\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8a37121 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"8a37121\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2e430cd elementor-widget elementor-widget-heading\" data-id=\"2e430cd\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">6. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow3}\\frac{arc\\tan\\left(x-3\\right)}{x^2-9}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-25af037 e-con-full e-flex e-con e-child\" data-id=\"25af037\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8ae4568 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"8ae4568\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2d44cf0 elementor-widget elementor-widget-heading\" data-id=\"2d44cf0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">7. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow0^-}\\frac{e^x-1}{\\cos\\left(x\\right)-1}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9b116fa e-con-full e-flex e-con e-child\" data-id=\"9b116fa\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9d09404 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"9d09404\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-27b86a4 elementor-widget elementor-widget-heading\" data-id=\"27b86a4\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">8. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow e}\\frac{1-\\ln\\left(x\\right)}{\\ln\\left(\\ln\\left(x\\right)\\right)}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b8cf35c e-con-full e-flex e-con e-child\" data-id=\"b8cf35c\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3f2867c elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"3f2867c\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-115b552 elementor-widget elementor-widget-heading\" data-id=\"115b552\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">9. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow\\infty}\\frac{\\ln\\left(\\ln\\left(x\\right)\\right)}{2x^2-9}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-16f08cb e-con-full e-flex e-con e-child\" data-id=\"16f08cb\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7ce4690 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"7ce4690\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-908a69f elementor-widget elementor-widget-heading\" data-id=\"908a69f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">10. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow\\infty}\\frac{arcctg\\left(x\\right)}{e^{-x}}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-200d6dd e-con-full e-flex e-con e-child\" data-id=\"200d6dd\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-76ddf7b elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"76ddf7b\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fregula-de-lhospitala%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9f83ca6 elementor-widget elementor-widget-heading\" data-id=\"9f83ca6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">11. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow-\\infty}e^\\frac{x^4+2x^2-1}{3x^2-5x+4}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9c1922c e-con-full e-flex e-con e-child\" data-id=\"9c1922c\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c9449eb elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"c9449eb\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h4 id=\"elementor-tab-title-2111\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2111\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><svg class=\"elementor-toggle-icon-opened e-font-icon-svg e-fas-caret-up\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">rozwi\u0105zanie<\/a>\n\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2111\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2111\"><p>$$\\lim_{x\\rightarrow\\mathrm\\pi^+}\\frac{\\ln\\left(x-\\mathrm\\pi\\right)}{\\mathrm{tgx}}=\\lim_{x\\rightarrow\\mathrm\\pi^+}\\frac{\\left(\\ln\\left(x-\\mathrm\\pi\\right)\\right)&#8217;}{\\left(\\mathrm{tgx}\\right)&#8217;}=\\lim_{x\\rightarrow\\mathrm\\pi^+}\\frac{\\displaystyle\\frac1{x-\\mathrm\\pi}}{\\displaystyle\\frac1{\\cos^2x}}=\\\\\\lim_{x\\rightarrow\\mathrm\\pi^+}\\frac{\\cos^2x}{x-\\mathrm\\pi}=\\frac{\\left(-1\\right)^2}{0^+}=\\frac1{0^+}=\\infty$$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-561b0c0 elementor-widget elementor-widget-heading\" data-id=\"561b0c0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">12. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow\\mathrm\\pi^+}\\frac{\\ln\\left(x-\\mathrm\\pi\\right)}{\\mathrm{tgx}}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-84b9bd0 e-con-full e-flex e-con e-child\" data-id=\"84b9bd0\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-85e0be5 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"85e0be5\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h4 id=\"elementor-tab-title-1401\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1401\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><svg class=\"elementor-toggle-icon-opened e-font-icon-svg e-fas-caret-up\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">rozwi\u0105zanie<\/a>\n\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1401\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1401\"><p>$$\\lim_{x\\rightarrow0}\\frac{\\sin\\left(2x\\right)-2x}{2x^3}=^{l&#8217;H}\\lim_{x\\rightarrow0}\\frac{\\left(\\sin\\left(2x\\right)-2x\\right)&#8217;}{\\left(2x^3\\right)&#8217;}\\\\=\\lim_{x\\rightarrow0}\\frac{\\cos\\left(2x\\right)\\cdot2-2}{6x^2}=^{l&#8217;H}\\lim_{x\\rightarrow0}\\frac{\\left(\\cos\\left(2x\\right)\\cdot2-2\\right)&#8217;}{\\left(6x^2\\right)&#8217;}\\\\=\\lim_{x\\rightarrow0}\\frac{-4\\sin\\left(2x\\right)}{12x}=^{l&#8217;H}\\lim_{x\\rightarrow0}\\frac{\\left(-4\\sin\\left(2x\\right)\\right)&#8217;}{\\left(12x\\right)&#8217;}\\\\\\lim_{x\\rightarrow0}\\frac{-8\\cos\\left(2x\\right)}{12}=-\\frac8{12}=-\\frac23$$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-35eee26 elementor-widget elementor-widget-heading\" data-id=\"35eee26\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">13. Stosuj\u0105c regu\u0142\u0119 de l'Hospitala oblicz granic\u0119:$$\\lim_{x\\rightarrow0}\\frac{\\sin\\left(2x\\right)-2x}{2x^3}$$<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>zarejestruj si\u0119 POCHODNE Regu\u0142a de l&#8217;Hospitala Je\u015bli licz\u0105c granic\u0119 funkcji (frac{fleft(xright)}{gleft(xright)}) wychodzi nam: (frac00 lub;fracinftyinfty), to liczymy granic\u0119: (frac{f&#8217;left(xright)}{g&#8217;left(xright)}) KLIKNIJ TUTAJ WZORY: Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 1.Stosuj\u0105c regu\u0142\u0119 de l&#8217;Hospitala oblicz granic\u0119:$$lim_{xrightarrowinfty}frac{lnleft(xright)}x$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 2.Stosuj\u0105c regu\u0142\u0119 de l&#8217;Hospitala oblicz granic\u0119:$$lim_{xrightarrowinfty}frac{e^x}x$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 3. Stosuj\u0105c regu\u0142\u0119 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/landing.php","meta":{"pmpro_default_level":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"class_list":["post-3045","page","type-page","status-publish","hentry","pmpro-has-access","entry","owp-thumbs-layout-horizontal","owp-btn-normal","owp-tabs-layout-horizontal","has-no-thumbnails","has-product-nav"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/3045","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/comments?post=3045"}],"version-history":[{"count":49,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/3045\/revisions"}],"predecessor-version":[{"id":4579,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/3045\/revisions\/4579"}],"wp:attachment":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/media?parent=3045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}