Please Explain what is meant by this?

Question

what is meant by

limit of f(x)= -4 as x approaches 3?

thanks

Answer 1

It means that as your graph aproaches the x value which is 3 in this case, the y axis aproaches the limit which in this case is -4

Answer 2

The other posts have given you a general idea of what the limit is all about. There is a precise technical mathematical definition, however, and I am going to give you that one.

We say that the limit of f(x) = -4 as x approaches 3 if given any arbitrarily small positive number epsilon (I will write it as e), there is a positive number delta (I will write it as d), such that:

whenever | x - 3 | < d, then | f(x) - -4 | < e

(note that the | | are absolute values).

So the idea is that if we can make f(x) as close to -4 as we want by choosing x close enough to 3, then we say that the limit of f(x) as x approaches 3 is -4.

As an example, let's suppose that f(x) = x - 7.

Then if I say that I want | f(x) + 4 | < e, then

| f(x) + 4 | = | x - 7 + 4 | = | x - 3 | < e

So if I choose d = e, I have | x - 3 | < d, and the requirements for the definition of a limit are satisfied. I can then say that the that the limit of f(x) = x-7 as x approaches 3 is -4.

This might seem like a complicated way to explain the limit, but it is needed when you get to proofs involving limits.

Answer 3

Consider a function f defined for values of x, as x gets close to a number a, not necessarily true for x = a. If the value of f(x) approaches a number b as x approaches a, then the limit of f(x) as x approaches a is equal to b, denoted as :

lim x---->a f(x) = b

ex.
Find the limit of f(x) = 3x + 2 as x approaches 3.

It is said that as x approaches 3, 3x approaches 9, and 3x + 2 approaches 11. Thus;

limx®3 3x + 2 = 11

Find the limit of f(x) = 1/ x - 3 as x approaches 3.

It is said that as x approaches 3, x - 3 approaches 0, and 1/ x - 3 approaches 1/ 0 which is undefined. Thus;

limx®3 1/x - 3 = undefined

In limits, the only thing that matters is how a function is defined near the point a.



that was an example hope i helped

Answer 4

uhhh im guessing it looks like this

limit f(x) =-4
x->3

that just means as x approaches to 3 the limit of f(x) = -4
im supposing the question has a graph or function that goes with it.

Answer 5

If you want a arbitrary verbal definition,

lim f(x) = -4
x -> 3

It means that as x gets really close to (but not equal to) 3, f(x) gets really close to (but not equal to) -4.

Limits are, in essence, approximations. As x gets arbitrarily close to 3, f(x) gets arbitrarily close to -4.

Answer 6

ok as the value of x becomes a number closer and closer to 3, the solution to the equation f(x) (whatever it may be) becomes closer to -4.