what is limit in mathematics?

Relevance

Limit means ' TENDS TO'

For ex: if i say lim x --> 0 f(x), than tat means wat will be the value of the function when x reaches virtually '0' though not exactly.

Like, wat u will say 0.00000000000008 = 0. Right? Well as u can see though its not exactly '0' but its virtually tends to be '0'. Thats wat we call limit.

If i say lim x --> 5, f(x) = 2x, than the answer will be '10'. Though the exact answer may be somewhere near '10', but for practical purpose u will say it as 10.

Hope u have got it.

Enjoy Maths. :-)

• 4 years ago

Math is a language with set guidelines and set meanings and a fashion of creating new meanings out of the former. Human coloquial languages consisting of English, are continually in flux so that you're by no skill particular no matter if a note skill what you commonly use the note for or has a diverse or broarder which skill. Godel and others have discovered barriers in formal matematical languages, at the same time as Fodor and others have discovered barriers in usual languages about issues contained in the genuine international. They both have their strengths and weak spot, yet surely usual language is imprecise yet huge accomplishing at the same time as Math has a tendency to be narrower yet extra sturdy.

In mathematics, the limit of a function is a fundamental concept in mathematical analysis. Informally, a function f has limit L at a point p when we can make the value of f as close to L as we want, by taking points close enough to p. Formal definitions, first devised around the end of the 19th century, are given below.

To motivate the definition of a limit, consider the following informal statement:

A real-valued function f(x) has limit L as x approaches the real number c if the values of f(x) become closer and closer to L as the value of x gets closer and closer to c.

To contextualize this informal statement, imagine a traveler walking along the graph of y=f(x). Her horizontal position is measured by the value of x: this is like the position given by a map of the land or by a global positioning system. Her altitude is given by the coordinate y. She is walking towards the horizontal position given by x=c. As she does so, she notices that her altitude approaches L. If later asked to guess the altitude over x=c, she would then answer L, even if she had never actually reached that position.

What, then, does it mean to say that her altitude approaches L? It means that her altitude gets nearer and nearer to L. In other words, she gets close to L except for a possible small error in accuracy. For example, suppose we set a particular accuracy goal for our traveler: she must get within a meter of L. She reports back that indeed she can get within one meter: she notes that when she is within five meters from x=c, her altitude is always one meter or less from L. We then change our accuracy goal: can she get within one centimeter? Yes. If she is within seven centimeters of x=c, then her altitude remains within one centimeter of the target L. In summary, to say that the traveler's altitude approaches L as her horizontal position approaches c means that for every target accuracy goal, there is some neighborhood of c whose altitude remains within that accuracy goal.

The initial informal statement can now be explicated

The limit of a function f(x) as x approaches c is a number L with the following property: given any target neighborhood of L, there is a neighborhood of c over which the values of f(x) remain within the target neighborhood.

This explicit statement is quite close to the formal definition of the limit of a function with values in a Hausdorff topological space.

Ultimate value a function is expected to reach is its limit. For eg as the number of sides in an equipolygon tends to infinity the polygon will tend to be a circle. In other words a circle can be viewed as a polygon of infinite number of sides!

limit means tends to

for example when we consider a function the value of the limit will be given.when we substitute the value we get the value of the function

this is limit meansthat is a function approaches a value

there are no limit in mathematics, today still so many theorem that people use in math but it's still cannot be proven, for example in theory number there are still lot of theory that sill need to proof so let discover that.. :-)

It's the value that a series or expression converges on as the independent variable approaches a given value.

Doug