## 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 $$f\left( x \right)$$ be a real valued function if the value of the function $$f\left( x \right)$$ approaches a… Click here to read more

If $$f$$ is a real valued function, then $$x$$ can approach $$a$$ from two sides: the left side of $$a$$… Click here to read more

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

In this tutorial we shall look at the limit of a polynomial function of any degree, and this is useful… Click here to read more

In this tutorial we shall derive the limit of a radical expression. These types of limits are usually solved by… Click here to read more

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

So far we have discussed limits at some fixed numbers. In this section we shall be concerned with limits at… Click here to read more

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

In this tutorial we shall discuss an example related to the limit of a function at positive infinity, i.e. $$x… Click here to read more

In this tutorial we shall discuss an example related to the limit of a function at negative infinity, i.e. $$x… Click here to read more

In this tutorial we shall discuss an example related to the limit at negative infinity with the radial form of… Click here to read more

In this tutorial we shall discuss an example related to the limit at positive infinity with the radial form of… Click here to read more

In this tutorial we shall discuss the very important formula of limits, \[\mathop {\lim }\limits_{x \to \infty } {\left( {1… Click here to read more

In this tutorial we shall discuss another very important formula of limits, \[\mathop {\lim }\limits_{x \to 0} \frac{{{a^x} – 1}}{x}… Click here to read more

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

In this tutorial we shall discuss an example of evaluating limits involving radical expressions. In most cases, if the limit… Click here to read more

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

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

A moving physical object cannot vanish at one 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

Let A and B be any two non–empty sets. Then a function ‘$$f$$’ is a rule or law which associates… Click here to read more

Example: Find the range of the function $$f\left( {\text{x}} \right) = \frac{{{\text{x}} + 1}}{{{\text{x}} – 1}}$$. Solution: We have \[f\left(… Click here to read more

Constant Function: Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘$$f$$’ from ‘A’ to ‘B’ is… Click here to read more

One – One Function: Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘$$f$$’ from A to… Click here to read more

Meaning of the Phrase “Tend to Zero”: Suppose a variable ‘x’ assumes in succession a set of values. \[1,\;\frac{1}{{10}},\;\frac{1}{{{{10}^2}}},\;\frac{1}{{{{10}^3}}},\;\frac{1}{{{{10}^4}}},\; \cdots… Click here to read more

Example: If $$f\left( {\text{x}} \right) = {{\text{x}}^3} – 2{{\text{x}}^2} + 3{\text{x}} – 7$$, then evaluate the limit $$\mathop {\lim }\limits_{{\text{x}} \to… Click here to read more