Situations with No Limit

[Jason76]

State three situations in which a limit doesn't exist:

1. jump in the graph (\(\displaystyle \lim x\rightarrow a- \neq \lim x \rightarrow a+\))

2. hole in the graph This might be wrong because, while it is discontinuous, there still is a limit. (\(\displaystyle \lim x\rightarrow a- = \lim x \rightarrow a+\))

3. asymptotic discontinuity (a vertical tangent), obviously no limit here, as infinity has no limit.

Any idea on another situation where a limit doesn't exist?

 

[Jason76]

My professor said today:

1. The limit from the left does not equal the limit from the right at x=a

2. The function is unbounded at x=a (or has a vertical asymptote there or the limit goes
to +/- infinity)

3. The function oscillates wildly at x=a

What does

3. The function oscillates wildly at x=a

mean?

In regards to 2, If it has a vertical asymptote, then it goes toward +/- infinity. There couldn't be a situation where it has a vertical asymptote, and it does NOT go toward +/- infinity. That's what he meant, right?

What does unbounded at x = a mean? Is that also referring to a vertical asymptote?

 

[JeffM]

My professor said today:



What does

mean?

In regards to 2, If it has a vertical asymptote, then it goes toward +/- infinity. There couldn't be a situation where it has a vertical asymptote, and it does NOT go toward +/- infinity. That's what he meant, right?

What does unbounded at x = a mean? Is that also referring to a vertical asymptote?

All of those are different ways of saying the same thing.