Limits (An Introduction)Limit of a functionLet y = f(x) be a function of x. If at x = a, f(x) takes indeterminate form, then we consider the values of the function which are very near to ‘a’. If these values tend to a definite unique number as x tends t…

MatricesDefinition A rectangular arrangement of numbers (which may be real or complex numbers) in rows and columns, is called a matrix. This arrangement is enclosed by small ( ) or big [ ] brackets. The numbers are called the elements of the matrix or en…

Standard Deviation and VarianceStandard DeviationStandard deviation (or S.D.) is the square root of the arithmetic mean of the square of deviations of various values from their arithmetic mean and is generally denoted by σ read as sigma. It is used in st…

Solving Polynomials Equations of Higher Degree When the powers in polynomial equations increase, it becomes more difficult to find their solutions (roots).Consider an equation such as Finding the roots of an equation such as this can prove to be quite a…

Integration by Parts (1) When integrand involves more than one type of functions: We may solve such integrals by a rule which is known as integration by parts. We know that, i.e., the integral of the product of two functions = (First function) × (Integr…

Exponential SeriesExponential SeriesDefinition (The number e) The limiting value of \({ \left( 1+\frac { 1 }{ n }  \right)  }^{ n }\) when n tends to infinity is denoted by e. Properties of e(1) e lies between 2.7 and 2.8. i.e., 2.7 < e < 2.8. (…

Sets and Venn DiagramsSet: A set is well defined class or collection of objects. Venn-Euler diagramsThe combination of rectangles and circles are called Venn-Euler diagrams or simply Venn-diagrams. If A and B are not equal but they have some common ele…

What is a Linear Regression Model?Linear regressionIf a relation between two variates x and y exists, then the dots of the scatter diagram will more or less be concentrated around a curve which is called the curve of regression. If this curve be a strai…

Quartiles and Box and Whisker PlotsWhen describing a set of data, without listing all of the values, we have seen that we can use measures of location such as the mean and median. It is also possible to get a sense of the data’s distribution by examinin…

SurdsDefinition of surdAny root of a number which can not be exactly found is called a surd. Let a be a rational number and n is a positive integer. If the nth root of x i.e., x1/n is irrational, then it is called surd of order n. Order of a surd is indi…