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Basic Definitions Constant: It is a symbol which retains the same value throughout a set of mathematical operations. Constant are of two types: Absolute and arbitrary Constant of the type 15, 7, -100 ete. do not change whatever We May perform are known as absolute constants Whereas m and ¢ in the equation) 7" « ot particular straight line but v a straight line are arbitrary constants as these remain fixed for a ary from straight ling to straight line. Variable: A variable is a quantity which is capable of taking various numerical values Variables are of Wo types Dependent and Independent Consider the equation y los. it Which x can take any value, 1 independent variable and 3 but for each value of vs there exist a value of yy. Here \ ts callec whose value depends upon that of x is called dependent variable. » according to some law are 5° related that AE inetion: If two variable quantities» and y \ . 5 said to be a value of y) can be obtained, then 3 corresponding to each value © fy only one function of y. {and the radius 7. Since Joan. We say f=rr’ is a rule that tells how to When we study circles, we usually call the are f(r). The equation « 4 for cach possible input value of the radius 7. that 1 is a function of rie. A calculate a unique output value of bles (the values for which the The set of all possible values of independent va Domai alled the domain of the function. function is defined) is ¢ Range: The set of all possible output of the dependent variable is called the range of the function. VE Limit of a functi , . ly Limit of a function: When « approaches a constant quantity from cither side, if there exists a definite finite number /, towards which / (0) approaches such that the numerical difference of f(x) and / can be made as small as we please by taking » sufficiently close to uw then | is defined as the limit of { (x) as © tends to «. This is symbolically written as lim /(x)=é. tow \, Continuity of a function: Geometrically, If the graph ofa function y= f (x) is a continuous curve we naturally call the function a continuous one. It means there should not be any sudden change in the value of the function i.e. a small change in the value of should produce a small change in the value of y and so the graph ‘of the function should be a continuous curve without any break in it. Differen Differentiation is an operator that calculate the rate of change of dependent variable with respect to independent variable and it is denoted by a ffealme) Shoionuecilnnexe2y Page Lot 46 ox: TWos fo) ><. 
