**Category : **JEE Main & Advanced

There are four types of interval:

(1) **Open interval :** Let *a* and *b* be two real numbers such that \[a<b\], then the set of all real numbers lying strictly between \[a\] and \[b\] is called an open interval and is denoted by \[[a,\,\,b]\] or \[(a,\,\,b)\]. Thus, \[[a,\,\,b]\] or \[(a,\,\,b)=\{x\in R\,:\,a<x<b\}\].

(2)** Closed interval :** Let *a* and *b* be two real numbers such that \[a<b,\] then the set of all real numbers lying between \[a\] and \[b\] including \[a\] and \[b\] is called a closed interval and is denoted by \[[a,\,\,b]\]. Thus, \[[a,\,\,b]=\{x\in R\,:\,a\le x\le b\}\]

(3) **Open-Closed interval : **It is denoted by \[[a,\,\,b]\] or \[(a,\,\,b]\] and \[[a,\,\,b]\] or \[(a,\,\,b]=\{x\in R\,:\,\,a<x\le b\}\].

(4) **Closed-Open interval : **It is denoted by \[[a,\,\,b]\] or \[[a,\,\,b)\] and \[[a,\,\,b]\] or \[[a,\,\,b)=\{x\in R\,:\,\,a\le x<b\}\]

*play_arrow*Some Important Definitions*play_arrow*Intervals*play_arrow*Definition of Function*play_arrow*Domain, Co-domain and Range of Function*play_arrow*Algebra of Functions*play_arrow*Kinds of function*play_arrow*Even and Odd Function*play_arrow*Periodic Function*play_arrow*Composite Function*play_arrow*Inverse Function*play_arrow*Limit of a Function*play_arrow*Fundamental Theorems on Limits*play_arrow*Methods of Evaluation of Limits*play_arrow*Introduction*play_arrow*Continuity of a Function at a Point*play_arrow*Continuity From Left and Right*play_arrow*Discontinuous Function*play_arrow*Differentiability of a Function at a Point

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