{"id":1942,"date":"2024-02-22T11:41:54","date_gmt":"2024-02-22T11:41:54","guid":{"rendered":"https:\/\/bezwarunku.pl\/?page_id=1942"},"modified":"2024-05-15T10:55:58","modified_gmt":"2024-05-15T09:55:58","slug":"granice-funkcji-z-funkcja-trygonometryczna-2","status":"publish","type":"page","link":"https:\/\/bezwarunku.pl\/index.php\/granice-funkcji-z-funkcja-trygonometryczna-2\/","title":{"rendered":"granice funkcji z logarytmem lub liczb\u0105 e"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1942\" class=\"elementor elementor-1942\" data-elementor-post-type=\"page\">\n\t\t\t\t<header class=\"elementor-element elementor-element-e841124 e-con-full e-flex e-con e-parent\" data-id=\"e841124\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-41e26b7 e-con-full e-flex e-con e-child\" data-id=\"41e26b7\" 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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-6b5607e e-con-full e-flex e-con e-parent\" data-id=\"6b5607e\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-da21d8f elementor-widget elementor-widget-heading\" data-id=\"da21d8f\" 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-724b698 animated-slow elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"724b698\" 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\">GRANICE FUNKCJI Z LOGARYTMEM LUB LICZB\u0104 e<\/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-3c16de7 e-flex e-con-boxed e-con e-parent\" data-id=\"3c16de7\" 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-7bdea1f elementor-widget elementor-widget-heading\" data-id=\"7bdea1f\" 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<h1 class=\"elementor-heading-title elementor-size-default\">$$\\lim_{x\\rightarrow\\begin{array}{c}+\\\\-\\end{array}\\infty}\\left(1+\\frac ax\\right)^x=e^a$$<\/h1>\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-fe5c1b6 e-flex e-con-boxed e-con e-parent\" data-id=\"fe5c1b6\" 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-22c61a0 e-con-full e-flex e-con e-child\" data-id=\"22c61a0\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1a41a0c elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"1a41a0c\" 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-funkcji-z-funkcja-trygonometryczna-2%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-9bb42b4 elementor-widget elementor-widget-heading\" data-id=\"9bb42b4\" 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 funkcji: $$\\lim_{n\\rightarrow\\infty}\\left(1+\\frac1n\\right)^{3n}$$<\/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-a2b9366 e-con-full e-flex e-con e-child\" data-id=\"a2b9366\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5f3958f elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"5f3958f\" 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-funkcji-z-funkcja-trygonometryczna-2%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-9934bec elementor-widget elementor-widget-heading\" data-id=\"9934bec\" 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 funkcji: $$\\lim_{n\\rightarrow\\infty}\\left(1+\\frac1{5n}\\right)^{2n+6}$$<\/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-1524347 e-con-full e-flex e-con e-child\" data-id=\"1524347\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f37f8f4 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"f37f8f4\" 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-funkcji-z-funkcja-trygonometryczna-2%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-ef5baa1 elementor-widget elementor-widget-heading\" data-id=\"ef5baa1\" 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 funkcji: $$\\lim_{n\\rightarrow\\infty}\\left(1+\\frac7{3n}\\right)^{n-1}$$<\/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-8f1e329 e-con-full e-flex e-con e-child\" data-id=\"8f1e329\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7f02d41 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"7f02d41\" 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-funkcji-z-funkcja-trygonometryczna-2%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-58d5515 elementor-widget elementor-widget-heading\" data-id=\"58d5515\" 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 funkcji: $$\\lim_{n\\rightarrow\\infty}\\left(\\frac{2n+1}{2n+3}\\right)^n$$<\/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-6833e87 e-con-full e-flex e-con e-child\" data-id=\"6833e87\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2ecf707 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"2ecf707\" 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-funkcji-z-funkcja-trygonometryczna-2%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-cdee971 elementor-widget elementor-widget-heading\" data-id=\"cdee971\" 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 funkcji: $$\\lim_{n\\rightarrow\\infty}\\left(\\frac{n+5}{n+4}\\right)^{2n-1}$$<\/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-3422a9a e-con-full e-flex e-con e-child\" data-id=\"3422a9a\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-accc50a elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"accc50a\" 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-funkcji-z-funkcja-trygonometryczna-2%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-fdd984c elementor-widget elementor-widget-heading\" data-id=\"fdd984c\" 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 funkcji: $$\\lim_{x\\rightarrow\\infty}\\left(\\frac{2n+5}{2n}\\right)^{3n-7}$$<\/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-7e0c9a5 e-con-full e-flex e-con e-child\" data-id=\"7e0c9a5\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3463c36 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"3463c36\" 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-funkcji-z-funkcja-trygonometryczna-2%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-44a1fc1 elementor-widget elementor-widget-heading\" data-id=\"44a1fc1\" 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 funkcji: $$\\lim_{x\\rightarrow\\infty}\\left(\\frac{2n+1}{2n-3}\\right)^{3n}$$<\/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-6732642 e-con-full e-flex e-con e-child\" data-id=\"6732642\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-434d1ec elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"434d1ec\" 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-funkcji-z-funkcja-trygonometryczna-2%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-88d9cf5 elementor-widget elementor-widget-heading\" data-id=\"88d9cf5\" 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 funkcji: $$\\lim_{x\\rightarrow\\infty}\\left(\\frac{n-1}{n+3}\\right)^{5-4n}$$<\/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-528ba4f e-con-full e-flex e-con e-child\" data-id=\"528ba4f\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1c04622 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"1c04622\" 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-funkcji-z-funkcja-trygonometryczna-2%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-0f787e8 elementor-widget elementor-widget-heading\" data-id=\"0f787e8\" 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 funkcji: $$\\lim_{x\\rightarrow\\infty}\\left(\\frac{6+4n}{2+4n}\\right)^{3-2n}$$<\/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-068bd38 e-con-full e-flex e-con e-child\" data-id=\"068bd38\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fc1c4f2 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"fc1c4f2\" 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-funkcji-z-funkcja-trygonometryczna-2%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-df34e84 elementor-widget elementor-widget-heading\" data-id=\"df34e84\" 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 funkcji: $$\\lim_{x\\rightarrow\\infty}\\left(\\frac{7n+10}{1+7n}\\right)^\\frac n3$$<\/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-ee484c7 e-flex e-con-boxed e-con e-parent\" data-id=\"ee484c7\" 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-3af4720 elementor-widget elementor-widget-heading\" data-id=\"3af4720\" 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<h1 class=\"elementor-heading-title elementor-size-default\">$$\\lim_{x\\rightarrow0}\\frac{a^x-1}x=\\ln a$$\n$$\\lim_{x\\rightarrow0}\\frac{\\ln\\left(1+x\\right)}x=1$$\n$$\\lim_{x\\rightarrow0}\\frac{\\log_a\\left(1+x\\right)}x=\\frac1{\\ln a}$$<\/h1>\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-da8da66 e-flex e-con-boxed e-con e-parent\" data-id=\"da8da66\" 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-91b7e4c e-con-full e-flex e-con e-child\" data-id=\"91b7e4c\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e288d7d elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"e288d7d\" 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-funkcji-z-funkcja-trygonometryczna-2%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-c71c4b6 elementor-widget elementor-widget-heading\" data-id=\"c71c4b6\" 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 funkcji: $$\\lim_{x\\rightarrow0}\\frac{\\ln\\left(1+3x\\right)}x$$<\/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-fc16f6e e-con-full e-flex e-con e-child\" data-id=\"fc16f6e\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-510b5e3 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"510b5e3\" 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-funkcji-z-funkcja-trygonometryczna-2%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-77e41fb elementor-widget elementor-widget-heading\" data-id=\"77e41fb\" 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 funkcji: $$\\lim_{x\\rightarrow0}\\frac{3^x-1}x$$<\/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-d89adbf e-con-full e-flex e-con e-child\" data-id=\"d89adbf\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8ec0d04 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"8ec0d04\" 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-funkcji-z-funkcja-trygonometryczna-2%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-65e59c6 elementor-widget elementor-widget-heading\" data-id=\"65e59c6\" 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 funkcji: $$\\lim_{x\\rightarrow0}\\frac{\\log_5\\left(1+2x\\right)}{2x}$$<\/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-3e7ee43 e-con-full e-flex e-con e-child\" data-id=\"3e7ee43\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b4d0dc9 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"b4d0dc9\" 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-funkcji-z-funkcja-trygonometryczna-2%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-acc9de8 elementor-widget elementor-widget-heading\" data-id=\"acc9de8\" 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 funkcji: $$\\lim_{x\\rightarrow0}\\frac{3^x-1}{6^x-1}$$<\/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-40d4931 e-con-full e-flex e-con e-child\" data-id=\"40d4931\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7f4e9b2 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"7f4e9b2\" 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-funkcji-z-funkcja-trygonometryczna-2%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-7ed0688 elementor-widget elementor-widget-heading\" data-id=\"7ed0688\" 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 funkcji: $$\\lim_{x\\rightarrow0}\\frac{\\log_7\\left(1+x^4\\right)}{x^3}$$<\/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\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>zarejestruj si\u0119 GRANICE GRANICE FUNKCJI Z LOGARYTMEM LUB LICZB\u0104 e $$lim_{xrightarrowbegin{array}{c}+\\-end{array}infty}left(1+frac axright)^x=e^a$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 1. Oblicz granic\u0119 funkcji: $$lim_{nrightarrowinfty}left(1+frac1nright)^{3n}$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 2. Oblicz granic\u0119 funkcji: $$lim_{nrightarrowinfty}left(1+frac1{5n}right)^{2n+6}$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 3. Oblicz granic\u0119 funkcji: $$lim_{nrightarrowinfty}left(1+frac7{3n}right)^{n-1}$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 4. Oblicz granic\u0119 funkcji: [&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-1942","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\/1942","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=1942"}],"version-history":[{"count":146,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/1942\/revisions"}],"predecessor-version":[{"id":4549,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/1942\/revisions\/4549"}],"wp:attachment":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/media?parent=1942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}