**Category : **JEE Main & Advanced

(1) **Real numbers : **Real numbers are those which are either rational or irrational. The set of real numbers is denoted by \[R\].

- (2) Related quantities : When two quantities are such that the change in one is accompanied by the change in other,
*e.,*if the value of one quantity depends upon the other, then they are called related quantities.

(3) **Variable: **A variable is a symbol which can assume any value out of a given set of values.

(i) **Independent variable : **A variable which can take any arbitrary value, is called independent variable.

(ii) **Dependent variable :** A variable whose value depends upon the independent variable is called dependent variable.

(4) **Constant : **A constant is a symbol which does not change its value, *i.e*., retains the same value throughout a set of mathematical operation. These are generally denoted by \[a,\,\,b,\,\,c\] etc. There are two types of constant, absolute constant and arbitrary constant.

(5) **Absolute value : **The absolute value of a number \[x,\] denoted by \[|x|,\] is a number that satisfies the conditions

** **

** **

\[|x|=\left\{ \begin{matrix} -x \\ \,\,0 \\ \,\,\,x \\ \end{matrix}\,\,\,\begin{matrix} \text{if} \\ \text{if} \\ \text{if} \\ \end{matrix}\,\,\begin{matrix} x<0 \\ x=0 \\ x>0 \\ \end{matrix}. \right.\] We also define \[|x|,\]as follows, \[|x|=\] maximum \[\{x,\,\,-x\}\] or \[|x|=\sqrt{{{x}^{2}}}\].

(6) **Fractional part : **We know that \[x\ge [x].\] The difference between the number \['x'\] and it’s integral value \['[x]'\] is called the fractional part of \[x\] and is symbolically denoted as \[\{x\}\]. Thus, \[\{x\}=x-[x]\]*e.g.,* if \[x=4.92\] then \[[x]=4\] and \[\{x\}=0.92\].

Fractional part of any number is always non-negative and less than one.

*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

You need to login to perform this action.

You will be redirected in
3 sec

Free

Videos

Videos