## Introduction to Functions

In mathematics, the term function is very famous. If we look at the historical background the term, function was first used... Click here to read more

From basic to higher mathematics

In mathematics, the term function is very famous. If we look at the historical background the term, function was first used... Click here to read more

Let be a real valued function if the value of the function approaches a fixed number say as approaches to... Click here to read more

If is a real valued function, then can approaches from two sides, the left side of and the right side... Click here to read more

In this tutorial we give the statements of theorems on limits which will be useful in evaluating the limits. (1)... Click here to read more

In this tutorial we shall give idea of limit of a polynomial function of any degree which is useful to... Click here to read more

In this tutorial we shall drive of limit of a radical expression, these types of limits usually solve by using... Click here to read more

In this tutorial we shall discuss the limit of a piecewise function. Let us consider an example of limit of... Click here to read more

So far we have been discussed limits at some fixed numbers, in this section we shall be concerned with the... Click here to read more

So far we have been discussed limits at some fixed numbers; in this section we shall be concerned with the... Click here to read more

In this tutorial we shall discuss an example relating with limit of a function at positive infinity, i.e. . Let... Click here to read more

In this tutorial we shall discuss an example relating with limit of a function at negative infinity, i.e. . Let... Click here to read more

In this tutorial we shall discuss an example relating with limit at negative infinity with radial form of function, i.e.... Click here to read more

In this tutorial we shall discuss an example relating with limit at positive infinity with radial form of function, i.e.... Click here to read more

In this tutorial we shall discuss very important formula of limit that is Let us consider the relation We shall... Click here to read more

In this tutorial we shall discuss another very important formula of limit that is Let us consider the relation Let... Click here to read more

In this tutorial we shall discuss an example of limit which involves quadratic function, and to find the value of... Click here to read more

In this tutorial we shall discuss an example to evaluating limits involving radicals expression, in most of the cases if... Click here to read more

In this tutorial we shall discuss an example to evaluating limits involving cubic expression, in most of the cases if... Click here to read more

In this tutorial we shall discuss an example to evaluating limits involving function with nth power of variable, in most... Click here to read more

A moving physical object cannot vanish at some point and reappear someplace else to continue its motion. Thus, we perceive... Click here to read more

Let’s take an example to find the continuity of a function at any given point. Consider the function of the... Click here to read more

In the seventeenth century, Sir Isaac Newton, an English mathematician (1642–1727), and Gottfried Wilhelm Leibniz, a German mathematician (1646–1716), considered... Click here to read more

A variable which can assign any value independently is called the independent variable, and the variable which depends on some independent... Click here to read more

Example: Let (a) Find the average rate of change of with respect to over the interval . (b) Find the... Click here to read more

Let be a given function of . Give to a small increment and let the corresponding increment of by ,... Click here to read more

Example: Find, by definition, the derivative of function with respect to . Solution: Let I. Change to and to II.... Click here to read more

The derivative of a constant function is zero. Now we shall prove this constant function with the help of definition... Click here to read more

The derivative of x is 1 (one). Now by definition or first principle we shall show that derivative of x... Click here to read more

Power Rule of derivative is an essential formula in differential calculus. Now we shall prove this formula by definition or... Click here to read more

It is given that two functions are in form and take derivative of sum of these two functions which is... Click here to read more

It is given that two functions are in form and take derivative of difference of these two functions which is... Click here to read more

To find a derivative of a function, consider the examples to elaborate the concept of derivative of a given function... Click here to read more

To find a derivative of square roots of a function. This can be proving by using derivative by definition or... Click here to read more

Product rule of derivative is . In words we can read as derivative of product of two functions is equal... Click here to read more

Product rule of derivative is . In words we can read as derivative of quotient of two functions is equal... Click here to read more

Composition of Two Functions: The composition of two functions and is defined as Chain Rule: If is differentiable at the... Click here to read more

Example 1: Differentiate with respect to using chain rule method. Let us consider , then . Applying chain rule, we... Click here to read more

In this tutorial we discuss basic formulas of differentiation for algebraic function. 1. , Where is any constant. 2. 3.... Click here to read more

We shall prove formula for derivative of sine function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of cosine function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of tangent function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of cotangent function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of secant function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of cosecant function using by definition or first principle method. Let us suppose that... Click here to read more

In this tutorial we shall discuss derivative of sine squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of cosine squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of tangent squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of cotangent squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of secant squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of cosecant squared function and its related examples. It can be proved by... Click here to read more