Find the limit of this function

In summary, the limit of a sequence is the point at which the sequence reaches its largest value. For continuous functions, the limit is the point at which the function reaches its smallest value.
  • #1
racer
39
0
Hey there

Find the lim of F(X) as X approaches zero

F(X) = 0/X ( Zero over X )

Thanks.
 
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  • #2
Well its a constant function equal to 0 for all values of x not equal to zero. So we can see the limit is equal to 0.
 
  • #3
You could also use l'Hopital and get the same answer as Gib_Z provided.
 
  • #4
Well its a constant function equal to 0 for all values of x not equal to zero. So we can see the limit is equal to 0.

You could also use l'Hopital and get the same answer as Gib_Z provided.

Yeah it is zero but I want the lim without L'Hopital rule, I want the solution using Algebra.
 
  • #5
Find the Lim of 0/X as X approaches zero.

0/X = X-X/X = X/X - X/X = 1-1 = 0
 
  • #6
alternatively you can say that if y is a member of the the Reals then 0*y=0 set y=1/x. While not wrong, your solution simply overcomplicates things.
 
  • #7
no matter what x is, the answer will always be 0. unless x = 0, then it is undefined. so you can say it is just approaching 0
 
  • #8
f(x) approaches L as x goes to a if and only if f(x_n) approaches L for any sequence of numbers x_n approaching a.

Let x_n be any sequence of numbers approaching 0. What is 0/x_n? What is the limit of that sequence.
 
  • #9
f(x) approaches L as x goes to a if and only if f(x_n) approaches L for any sequence of numbers x_n approaching a.

Let x_n be any sequence of numbers approaching 0. What is 0/x_n? What is the limit of that sequence.

I don't know anything about Sequence limits.
 
  • #10
But you ask of the limit of continuous functions?
 
  • #11
Do you know the definition of a limit? If so it is obviously zero.
 

What does it mean to "find the limit of a function"?

Finding the limit of a function is the process of determining the value that a function approaches as its input approaches a specific value. This value is often referred to as the "limit point" or "limit value".

Why is finding the limit of a function important?

Finding the limit of a function can help us understand the behavior of the function at certain points and can also help us determine if a function is continuous at a specific point.

What are the different ways to find the limit of a function?

There are several methods for finding the limit of a function, including direct substitution, factoring, and using algebraic manipulations. Additionally, we can use graphs or tables to approximate the limit of a function.

What are some common mistakes when finding the limit of a function?

One common mistake is assuming that a function is continuous at a specific point without properly evaluating the limit. Another mistake is using incorrect algebraic manipulations or not considering the possibility of a one-sided limit.

Are there any real-world applications of finding the limit of a function?

Yes, finding the limit of a function has real-world applications in fields such as physics, engineering, and economics. For example, in physics, the limit can be used to determine the speed of an object at a specific time, and in economics, it can be used to model the growth of a company or the demand for a product.

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