Limits, Mathematics

Limits

The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some particular point 'a'. The question is, if we give values to x which are nearer and nearer to 'a', will the values of f(x) come nearer and nearer to any particular value? Suppose we define a function f(x) as:

                            f(x) = 2x

It can be seen that as we give values to x which are nearer and nearer to 0, then the value of f(x) also comes nearer and nearer to 0.

If x approaches a value 'a', f(x) approaches some number L, then we say that the limit of f(x) approaches L. This is symbolically written as

1669_limit.png        is to be read as 'x approaches a'.

Sometimes we may allow x to take values which are larger and larger, without any limit. This is symbolically written as  1954_limit1.png (read as 'x approaches infinity'). If f(x) approaches a limit L as  1967_limit2.png , then we write

1129_limit3.png

In some cases, it may so happen that as x approaches a value, the value of the function f(x) may become larger and larger without any limit. This is symbolically written as:

21_limit4.png

Example 

Suppose f(x) = 2x2 - 1

As x approaches value 1, f(x) approaches the value 1,

739_limit5.png

This is graphically represented below.

Figure 

1862_limit6.png

Posted Date: 9/13/2012 6:19:36 AM | Location : United States







Related Discussions:- Limits, Assignment Help, Ask Question on Limits, Get Answer, Expert's Help, Limits Discussions

Write discussion on Limits
Your posts are moderated
Related Questions
I am here to tell you, Alex has a cold.

Solve -10 cos(3t )= 7 on [-2,5]. Solution Let's first get the inverse cosine portion of this problem taken care of. cos(3 t )= -  7/10            ⇒     3t = cos -1 ( - 7

When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years.  Find their present

Town x and town y were 270km apart. a car started from town x towards town y at a uniform speed of 60km/hr, while a motorcycle started from town y to town x at a uniform speed of 9

how to express 15/4 into percentage

the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2

How many integers satisfy the inequality |10(x+1)/x^2+2x+3|=1? Solution) first thing thats not an inequality, and second thing its very easy if thats the question. the LHS = |10/

Factor following polynomials.                               x 2 + 2x -15 Solution x 2 +2x -15 Okay since the first term is x 2 we know that the factoring has to ta

if two circles O and O''intersect in two points, A and B, the the line segment OO is what?

Poisson Probability Distribution -  It is a set of probabilities which is acquired for discrete events which are described as being rare. Occasions similar to binominal distri