{"id":1758,"date":"2024-02-21T11:07:16","date_gmt":"2024-02-21T11:07:16","guid":{"rendered":"https:\/\/bezwarunku.pl\/?page_id=1758"},"modified":"2024-05-15T10:44:19","modified_gmt":"2024-05-15T09:44:19","slug":"granice-ciagow","status":"publish","type":"page","link":"https:\/\/bezwarunku.pl\/index.php\/granice-ciagow\/","title":{"rendered":"granice ci\u0105g\u00f3w"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1758\" class=\"elementor elementor-1758\" data-elementor-post-type=\"page\">\n\t\t\t\t<header class=\"elementor-element elementor-element-455fba5 e-con-full e-flex e-con e-parent\" data-id=\"455fba5\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-389adb0 e-con-full e-flex e-con e-child\" data-id=\"389adb0\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ad64a9a elementor-widget 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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-c0e8567 e-con-full e-flex e-con e-parent\" data-id=\"c0e8567\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-775ae3e elementor-widget elementor-widget-heading\" data-id=\"775ae3e\" 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\">GRANICE<\/a><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-30549d0 animated-slow elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"30549d0\" 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\"><br><br>GRANICE CI\u0104G\u00d3W<\/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-5c12b16 e-flex e-con-boxed e-con e-parent\" data-id=\"5c12b16\" 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-ef1a92d e-con-full e-flex e-con e-child\" data-id=\"ef1a92d\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5ee651d elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"5ee651d\" 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%2Fgranice-ciagow%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-7b60679 elementor-widget elementor-widget-heading\" data-id=\"7b60679\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac n2$$<\/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-a44c1b0 e-con-full e-flex e-con e-child\" data-id=\"a44c1b0\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3cddd9c elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"3cddd9c\" 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%2Fgranice-ciagow%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-8aa0602 elementor-widget elementor-widget-heading\" data-id=\"8aa0602\" 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.Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{n+2}{2n+1}$$<\/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-142af54 e-con-full e-flex e-con e-child\" data-id=\"142af54\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-419775b elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"419775b\" 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%2Fgranice-ciagow%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-820931a elementor-widget elementor-widget-heading\" data-id=\"820931a\" 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.Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{2n^2(n-2)}{(1-3n)(2+n^2)}$$<\/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-fcbc487 e-con-full e-flex e-con e-child\" data-id=\"fcbc487\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3ad0148 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"3ad0148\" 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%2Fgranice-ciagow%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-7337716 elementor-widget elementor-widget-heading\" data-id=\"7337716\" 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.Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{1+3+5+...+(2n-1)}{2+4+6+...+2n}\\\\$$<\/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-3794f0f e-con-full e-flex e-con e-child\" data-id=\"3794f0f\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4849301 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"4849301\" 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%2Fgranice-ciagow%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-d87cfd4 elementor-widget elementor-widget-heading\" data-id=\"d87cfd4\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{1+2+3+...+n}{n^2}\\\\$$<\/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-722615c e-con-full e-flex e-con e-child\" data-id=\"722615c\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0976434 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"0976434\" 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-9921\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-9921\" 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-9921\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-9921\"><p>$$\\lim_{{x\\rightarrow\\infty}}\\left(-2n^5+3n^2-10\\right)=\\lim_{{x\\rightarrow\\infty}}n^5\\left(-2+\\frac{3}{n^3}-\\frac{10}{n^5}\\right)\\;(wyci\u0105gn\u0119li\u015bmy\\;n^5)<br \/>$$$$\\lim_{{n\\rightarrow\\infty}} n^5 \\left(-2^{\\nearrow^{-2}} + \\frac{3}{n^3}^{\\nearrow^0} &#8211; \\frac{10}{n^5}^{\\nearrow^0}\\right) = \\infty \\cdot (-2) = -\\infty<br \/>$$<\/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-f8a6870 elementor-widget elementor-widget-heading\" data-id=\"f8a6870\" 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.Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\left(-2n^5+3n^2-10\\right)$$<\/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-5bbe1b5 e-con-full e-flex e-con e-child\" data-id=\"5bbe1b5\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-33c5b72 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"33c5b72\" 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%2Fgranice-ciagow%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-269d229 elementor-widget elementor-widget-heading\" data-id=\"269d229\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\left(3n^4-\\frac3{n^3}+4n\\right)$$<\/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-9b693d1 e-con-full e-flex e-con e-child\" data-id=\"9b693d1\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0637e97 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"0637e97\" 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%2Fgranice-ciagow%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-dbb2dc8 elementor-widget elementor-widget-heading\" data-id=\"dbb2dc8\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{3-8n}{n+2}$$<\/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-804bf2c e-con-full e-flex e-con e-child\" data-id=\"804bf2c\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0e5a2f2 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"0e5a2f2\" 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%2Fgranice-ciagow%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-f1e48af elementor-widget elementor-widget-heading\" data-id=\"f1e48af\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{4n^2}{-n+2}$$<\/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-559aa92 e-con-full e-flex e-con e-child\" data-id=\"559aa92\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e17d1c6 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"e17d1c6\" 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%2Fgranice-ciagow%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-41fd27e elementor-widget elementor-widget-heading\" data-id=\"41fd27e\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{7n+2n^3}{7n^2-n-1}$$<\/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-72e250f e-con-full e-flex e-con e-child\" data-id=\"72e250f\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b935853 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"b935853\" 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-1941\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1941\" 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-1941\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1941\"><p>\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Wyci\u0105gamy w liczniku i mianowniku najwy\u017csz\u0105 pot\u0119g\u0119$$\\lim_{x\\rightarrow\\infty}\\frac{-3n^2+4n}{4n^3-n+2}=\\lim_{x\\rightarrow\\infty}\\frac{n^2\\left({\\displaystyle-3+\\frac4n}\\right)}{n^3\\left(4-{\\displaystyle\\frac1{n^2}}-{\\displaystyle\\frac2{n^3}}\\right)}=\\lim_{x\\rightarrow\\infty}\\frac{n^2}{n^3}\\cdot\\frac{\\displaystyle-3+\\frac4n}{4-\\frac1{n^2}-\\frac2{n^3}}=\\\\\\lim_{x\\rightarrow\\infty}\\frac1n^{\\nearrow^0}\\cdot\\frac{\\displaystyle-3^{\\nearrow^{-3}}+\\frac4n^{\\nearrow^0}}{4_{\\searrow_4}-{\\frac1{n^2}}_{\\searrow_0}-{\\frac2{n^3}}_{\\searrow_0}}=0\\cdot\\frac{-3}4=0$$<\/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-0547959 elementor-widget elementor-widget-heading\" data-id=\"0547959\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{-3n^2+4n}{4n^3-n+2}$$<\/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-e0b7e0e e-con-full e-flex e-con e-child\" data-id=\"e0b7e0e\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1194fa7 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"1194fa7\" 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%2Fgranice-ciagow%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-15000dc elementor-widget elementor-widget-heading\" data-id=\"15000dc\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\frac{\\left(n+3\\right)\\left(2n-1\\right)}{\\left(n-3\\right)^2}$$<\/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-1373355 e-con-full e-flex e-con e-child\" data-id=\"1373355\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9dc07bf elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"9dc07bf\" 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%2Fgranice-ciagow%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-957bc03 elementor-widget elementor-widget-heading\" data-id=\"957bc03\" 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. Oblicz granic\u0119 ci\u0105gu: $$\\lim_{x\\rightarrow\\infty}\\left(\\sqrt{n^2+5n}-\\sqrt{n^2+1}\\right)$$<\/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 GRANICE GRANICE CI\u0104G\u00d3W Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 1. Oblicz granic\u0119 ci\u0105gu: $$lim_{xrightarrowinfty}frac n2$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 2.Oblicz granic\u0119 ci\u0105gu: $$lim_{xrightarrowinfty}frac{n+2}{2n+1}$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 3.Oblicz granic\u0119 ci\u0105gu: $$lim_{xrightarrowinfty}frac{2n^2(n-2)}{(1-3n)(2+n^2)}$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 4.Oblicz granic\u0119 ci\u0105gu: $$lim_{xrightarrowinfty}frac{1+3+5+&#8230;+(2n-1)}{2+4+6+&#8230;+2n}\\$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 5. Oblicz [&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-1758","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\/1758","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=1758"}],"version-history":[{"count":172,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/1758\/revisions"}],"predecessor-version":[{"id":4543,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/1758\/revisions\/4543"}],"wp:attachment":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/media?parent=1758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}