Limit of Function: No Limit Found

In summary, the conversation discusses the existence of a limit for the given function, which involves using L'Hospital's rule and Maclaurin series to solve. However, it is determined that the function does not have a limit. The conversation also provides hints on how to approach the problem.
  • #1
Unskilled
12
0
could anyone tell me if this have a limit:
lim ((exp(x)-1-x)^2)/(x^2 - ln(x^2+1)))
x->0

My conclusion is that this doesn't have a limit. Tried everything, this is an problem that i run into.
 
Last edited:
Physics news on Phys.org
  • #2
Have you tried applying L'Hospital's?
 
  • #3
Unskilled said:
could anyone tell me if this have a limit:
lim ((exp(x)-1-x)^2)/(x^2 - ln(x^2+1)))
x->0

My conclusion is that this doesn't have a limit. Tried everything, this is an problem that i run into.
Have you tried using Maclaurin Series to solve this problem? :)
Hint:
The expansion of exp(x) arround x = 0 is:
[tex]e ^ x = 1 + x + \frac{x ^ 2}{2} + ...[/tex]
The expansion of ln(x + 1) arround x = 0 is:
[tex]\ln (x + 1) = x - \frac{x ^ 2}{2} + ...[/tex]
So what's the expansion of ln(x2 + 1) arround x = 0?
Can you go from here? :)
 

FAQ: Limit of Function: No Limit Found

What does it mean when the limit of a function is "no limit found"?

When the limit of a function is "no limit found", it means that as the independent variable approaches a certain value, the output of the function does not approach a specific value or tends to infinity. This can happen when the function is undefined or has a vertical asymptote at that specific value.

Can a function have a limit of "no limit found" at multiple points?

Yes, a function can have a limit of "no limit found" at multiple points. This can occur when the function has multiple vertical asymptotes or is undefined at multiple points.

How can a "no limit found" situation be graphically represented?

A "no limit found" situation can be graphically represented by a vertical asymptote or a point where the function is undefined. On a graph, this would appear as a vertical line or a hole in the graph.

Is it possible for a function to approach different values from the left and right but still have a limit of "no limit found"?

Yes, it is possible for a function to approach different values from the left and right but still have a limit of "no limit found". This can happen when the function has a jump or discontinuity at that specific value.

Can a function have a limit of "no limit found" at a point but still be continuous?

Yes, a function can have a limit of "no limit found" at a point but still be continuous. This can occur when the function has a removable discontinuity or a hole at that specific point.

Similar threads

Replies
10
Views
1K
Replies
4
Views
1K
Replies
5
Views
1K
Replies
11
Views
888
Replies
7
Views
1K
Replies
2
Views
267
Back
Top