Limits (1 Viewer)

[Lukybear]

Could some1 just explain to me when does a limit not exist? And how to prove it. I.e. lim *x>0* 1/x

In the book it says that as x>1 without restrictions from either below or above, lim f(x) does not exist.

 

[kurt.physics]

Could some1 just explain to me when does a limit not exist? And how to prove it. I.e. lim *x>0* 1/x

In the book it says that as x>1 without restrictions from either below or above, lim f(x) does not exist.

Here is a website that has video tutorials about limits and calculus in general. It will really help with your question =)

Tutorials for the Calculus Phobe

 

[Trebla]

A limit exists if has a well defined value. (i.e. it converges to a finite number)
As x approaches 0, then 1/x gets larger and larger without bound (it can get as large as it wants and does not appear to converge to a finite number).
Therefore, the limit doesn't exist. You can sketch the curve y = 1/x to visualise this.

 

[helpplease]

check the graph of 1/x and you can see that there can not be a two sided limit as x approaches zero because the graph of the function are going to opposite directions. therefore it does not exist. hope this helps. it also helps to know how the graphs look like

 

[Lukybear]

Another Question about limits:
Q: find the value of x where 0<|x-2|<x so that when x is restricted to this domain, the different between x^2 and 4 will be numerically smaller than a) 0.1 ... c) e where e>0

From the examples of this Q, to solve and find the answer that x-2 < e/5 and thus x = 0.02 etc... x was set less than 1 i.e.
1 < x <3 (as x approaches 2). Does this have to be the range?

 

[blaze.bluetane]

Best videos I have ever watched on limits.

Online Mathematics At The University of Houston

try videos 1 and 3

hope they help