Thread: Finding out if limits exist from a graph

1. Finding out if limits exist from a graph

I seem to be having some trouble grasping this concept. I want to know how I can tell if a limit exists by looking at a graph (cartesian plane) given specific points.

For instance I have the problem:

Given the points (0, -3) [its an open dot at this point] and (-2, -5) [a closed dot here] and y = h(x) determine the following limits (if they exist):

a. lim h(x)
x -> -2

b. lim h(x)
x -> 0

What math techniques can I use to approach a problem like this?

Thanks for any help.

2. If the function is defined at only two listed points (or maybe only the one?), there can be no limit, as far as I know.

Is any information provided regarding the function's behavior outside of the two listed points?

Thank you!

3. Originally Posted by stapel
If the function is defined at only two listed points (or maybe only the one?), there can be no limit, as far as I know.

Is any information provided regarding the function's behavior outside of the two listed points?

Thank you!
No additional information is provided about the function. All the information that is provided is listed as such in my post above.

Thanks.

4. Are you sure the graph does not consist of lines or curves with "points (0, -3) [its an open dot at this point] and (-2, -5) [a closed dot here]"? It hat is the case then the $\lim_{x\rightarrow 0}h(x)= -3$ and $\lim_{x\rightarrow -2}h(x)= -5$.

5. Originally Posted by HallsofIvy
Are you sure the graph does not consist of lines or curves with "points (0, -3) [its an open dot at this point] and (-2, -5) [a closed dot here]"? It hat is the case then the $\lim_{x\rightarrow 0}h(x)= -3$ and $\lim_{x\rightarrow -2}h(x)= -5$.
There is one line on this graph and it passes through the points I have given, and as I have said there's an open dot at the point (0,-3) and a closed dot at the other one. Does your limit existence still hold true now that you know this?

I'm pretty sure I understand what your trying to say. Thanks!

6. Originally Posted by hemi
There is one line on this graph and it passes through the points I have given, and as I have said there's an open dot at the point (0,-3) and a closed dot at the other one. Does your limit existence still hold true now that you know this?

I'm pretty sure I understand what your trying to say. Thanks!
You might consider telling us what you have been told an open and closed dots signify (we can guess, but it is good for you to practice giving all the information you have when asking for help). Also consider if there is some other contextural information, that you have that might make our job a bit easier, that we are unaware of which might make our job a bit easier.

CB