If the limit of a function is 2 , then what does it mean generally ? plz answer in simple language.?

Answer 1

Well Body
That means if your variable (for instant x ) get closer to 2
the function going to get closer to something else .
Be aware the variable is not going to be 2 just it is closing to 2 ( it can be 2.000001 or 1.9999999 but not 2)
In other word, put a number very close to 2 instead of "x" and then and then solve the function.

Answer 2

It means if you add terms an infinite number of times, you get to the answer 2.

For example, take the series 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/(2^n).

Counting just the first term, the sum is 1
Counting the first 2 terms, the sum is 1.5
Counting the first 3 terms, the sum is 1.75
Counting the first 4 terms, the sum is 1.875
Counting the first 5 terms, the sum is 1.9375
Counting the first 6 terms, the sum is 1.96875
Counting the first 7 terms, the sum is 1.983275
...

The series is getting bigger, but it will never exceed 2. It is approaching 2. If you can imagine adding all the terms, you would get a value of 2. So the limit (as n approaches infinity) is 2.

Stated another way, the sum is getting closer and closer to 2. The difference between 2 and the sum is getting infinitely smaller until it is indistinguishable from 2.

Answer 3

A function is a rule that takes a number you give it (input) and gives you a number back (output). The limit of a function describes how the function will behave when certain numbers are inputed into the function. As you continue to input values into the function, the closer the answer (output) comes to 2.

For example, lim 2/x as x approaches 1.... the limit will be 2.

Answer 4

Normally, when mathematicians talk about limits, they talk about something tending towards a limit.

Let's look first at the situation where the function is examined over a finite interval. In this case, for simplicity, consider the interval (0,1) (open interval), and let the function we are talking about be f(x) = 2x.
Then lim f(x) = 2.
x->1
(The left hand side of that equation is pronounced, "the limit of f(x) as x tends to 1.")

The same would be true if I considered a larger interval, e.g. [-1,5] (a closed interval this time). This is true whether you creep up on 1 from the left hand side i.e. a number smaller than 1, or whether you creep up on it from the right hand side, i.e. a number greater than 1.

Mathematicians are often interested in functions "as x tends to infinity".

As an example, let f(x) = 1/x + 2.

In this case,
lim f(x) = 2
x -> infinity
means that as x gets larger and larger, f(x) will get closer and closer to 2.

Hope this helps.

Answer 5

Doesn't mean anything really . lim x=2

Answer 6

the function will not be equal to two, but it will approach to it.