{"id":3180,"date":"2021-07-19T02:45:42","date_gmt":"2021-07-19T02:45:42","guid":{"rendered":"http:\/\/calculuscoaches.com\/?page_id=3180"},"modified":"2023-09-04T15:40:15","modified_gmt":"2023-09-04T15:40:15","slug":"example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-1","status":"publish","type":"page","link":"https:\/\/calculuscoaches.com\/index.php\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-1\/","title":{"rendered":"example of when a limit does not exist for a function of two variables 1"},"content":{"rendered":"\n<figure id=\"attachment_3186\" aria-describedby=\"caption-attachment-3186\" style=\"width: 1698px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3186 mBox\"  src=\"http:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed.jpg\" alt=\"\" width=\"1698\" height=\"941\" srcset=\"https:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed.jpg 1698w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed-300x166.jpg 300w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed-644x357.jpg 644w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed-768x426.jpg 768w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed-1536x851.jpg 1536w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2021\/07\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-with-detailed-graphs-and-paths-of-approached-graphed-600x333.jpg 600w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/a><figcaption id=\"caption-attachment-3186\" class=\"wp-caption-text\">example of when a limit does not exist for a function of two variables with detailed graphs and paths of approached graphed<\/figcaption><\/figure>\n\n\n\nThe function is defined as f(x, y) = x(ax\u00b2)\u00b2\/(x\u00b2+(ax\u00b2)\u2074). If we move towards the origin along the line y=x, we get the limit lim(x, y) \u2192 (0, 0) f(x, y) = 0. However, if we move towards the origin along the line y=mx, where m is not equal to 1, we get the limit lim(x, y) \u2192 (0, 0) f(x, y) = 0. This means that the limit of the function does not exist at the origin.\n\nThe reason for this is that the function has a sharp turn at the origin. As we move towards the origin along the line y=x, the function approaches 0 smoothly. However, as we move towards the origin along the line y=mx, the function approaches 0 in a sharp way. This is because the denominator of the function approaches 0 much faster than the numerator along the line y=mx.\n\nThis is an example of a function whose limit does not exist because it is not continuous at the origin. A function is continuous at a point if and only if the limit of the function at that point exists. In this case, the limit of the function does not exist because the function has a sharp turn at the origin.\n","protected":false},"excerpt":{"rendered":"<p>The function is defined as f(x, y) = x(ax\u00b2)\u00b2\/(x\u00b2+(ax\u00b2)\u2074). If we move towards the origin along the line y=x, we get the limit lim(x, y) \u2192 (0, 0) f(x, y) = 0. However, if we move towards the origin along the line y=mx, where m is not equal to 1, we get the limit lim(x, &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/calculuscoaches.com\/index.php\/example-of-when-a-limit-does-not-exist-for-a-function-of-two-variables-1\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;example of when a limit does not exist for a function of two variables 1&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":3186,"parent":0,"menu_order":85,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3180","page","type-page","status-publish","has-post-thumbnail","hentry"],"aioseo_notices":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages\/3180","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/comments?post=3180"}],"version-history":[{"count":2,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages\/3180\/revisions"}],"predecessor-version":[{"id":6675,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages\/3180\/revisions\/6675"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/media\/3186"}],"wp:attachment":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/media?parent=3180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}