{"id":5046,"date":"2012-12-12T05:41:56","date_gmt":"2012-12-12T05:41:56","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=5046"},"modified":"2014-12-02T08:27:06","modified_gmt":"2014-12-02T08:27:06","slug":"limits-reaching-for-a-goal","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/limits-reaching-for-a-goal\/","title":{"rendered":"Limits: Reaching for a Goal"},"content":{"rendered":"

A limit can be a difficult concept to grasp in mathematics, as it is a value that is never reached, but is ‘approached’ by an input, or index of some nature. Limits are essential for integrals, continuity and derivatives in calculus<\/a>.<\/p>\n

Let f(x) be a given function. Values of f(x) can be made arbitrarily close to L. We can do this by taking x sufficiently close to a, with x\u2260a, on either side of a, then we say that L is the limit of f(x) as x approaches a and we write it as \"\"<\/a>f(x) = L.<\/p>\n

If x\u00e0\u221e then it means that x values will go far on the right side of the horizontal axis, \u00a0x-axis. The corresponding f(x) values will be read on the vertical axis, Y-axis. To understand this we can examine the following examples.<\/p>\n

\"\"<\/a><\/p>\n

Calculation of limits:<\/strong><\/p>\n

a)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of sum of two functions is nothing but the sums of the limits of the individual functions.<\/p>\n

\"\"<\/a>[f(x)+g(x)] = \u00a0\"\"<\/a>f(x) + \u00a0\"\"<\/a>g(x)<\/p>\n

b)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of difference of two functions is nothing but the difference of the limits of the individual functions in the given order.<\/p>\n

\"\"<\/a>\u00a0\u00a0 \u00a0[f(x)-g(x)] = \"\"<\/a>\u00a0f(x) – \"\"<\/a>\u00a0g(x)<\/p>\n

c)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of product of two functions is nothing but the product of the limits of the individual functions.<\/p>\n

\"\"<\/a>[f(x)*g(x)] =\"\"<\/a> \u00a0f(x) * \"\"<\/a>g(x)<\/p>\n

d)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of quotient of two functions is nothing but the quotient of the limits of the individual functions in the given order.<\/p>\n

\"\"<\/a>[f(x)\/g(x)] =\"\"<\/a> \u00a0f(x)\/\"\"<\/a> g(x)<\/p>\n

Situations where a limit cannot be found:<\/strong><\/p>\n

a)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of a difference of functions cannot exist if both tend to \u221e.<\/p>\n

b)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of product of two functions cannot exist of one tend to \u221e and the other tend to 0.<\/p>\n

c)\u00a0\u00a0\u00a0\u00a0\u00a0 The limit of quotient of two functions cannot exist if both tend to either \u221e or zero.<\/p>\n

Need further help with Math<\/a>?<\/p>\n

 
\nSchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Delaware visit: Tutoring in Delaware. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

A limit can be a difficult concept to grasp in mathematics, as it is a value that is never reached, but is ‘approached’ by an input, or index of some nature. Limits are essential for integrals, continuity and derivatives in calculus. Let f(x) be a given function. Values of f(x) can be made arbitrarily close […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[4],"tags":[494,781,940,1037,1396,1467,1774,1819,1941],"class_list":["post-5046","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-difference","tag-horizontal","tag-infinty","tag-limit","tag-product","tag-quotient","tag-sum","tag-tend","tag-vertical"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5046","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=5046"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5046\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}