{"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":"http:\/\/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
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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":"

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, … <\/p>\n

Continue reading “example of when a limit does not exist for a function of two variables 1”<\/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":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t