Question

Question about a limit that equals infinity.

Answer 1

If a limit equals infinity what does that mean? Here was the dialect........

CALC THREE PROFESSOR: Recall from calc one what it means when a limit equals infinity....
Student: That means if does not exist.
CALC THREE PROFESSOR: But what does that mean? There was something very specific that you learned from calc one.
Student: I didn't have you for calc one, and my professor did not say anything other than a limit that equals infinity does not exist.
CALC THREE PROFESSOR: Then your professor did you an injustice and you need to revisit calc one.

Answer 2

Any idea what he may have been refering to?

Answer 3

We are in the beginning of a section dealing with vector valued functions and he was showing that the limit of a vector valued function was the limit of it's components. so the original vector was \[(\frac{ \sin(t) }{ t })i+(\frac{ \tan(t) }{ t })j+(\frac{ e^t }{ t })k\] and when he took the limit of the kth element it was an indeterminant form. Then using lhopitals you get the limit equals infinity, this is what led to the dialect I posted above.

Answer 4

all i can recall is that when a two sided limit both goes to the same infinity ... then it can be said to approach infinity

Answer 5

well when we take the limit of the vector valued function he wants us to give a result like:
3i+4j-5k
so the question is , I think, what do you put for the component when the limit equals infinity?

Answer 6

the limit as t approaches what?

Answer 7

\[x(t)=\frac{ \sin(t) }{ t }\\
y(t)=\frac{ \tan(t) }{ t }\\
z(t)=\frac{ e^t }{ t }\]
the limits as t approaches ....

Answer 8

infinity

Answer 9

yeah, i cant come to a solution either ....

Answer 10

I really don't know what to do for that situation either.

Answer 11

It means that the value is so large that it is best to assume infinity?

Answer 12

Or that a series converges to some number? I remember something about that in a course but I may have that wrong.

Answer 13

Yeah I had a calc teacher that said the same thing as the other student in my class. My professor used the delta epsilon proof to show simply that a limit that equals infinity does not exist. So I don't know what else to say other than that.

Answer 14

I don't remember how to use delta epsilon proof for multivariable limits.. But I assume it's the same as single-variable. Lol

Answer 15

Well that was what this professor said was that this concept came from calc one so we would be talking about single variable limits and my professor from calc one used delta epsilon proofs to show that a limit that equals infinity did not exist.

Answer 16

So I don't know what to do for this because I was taught the same: simply that when the result of evaluating a limit is infinity it does not exist.

Answer 17

A limit doesn't exist if it doesn't approach the same point. If it approaches the same infinity then ti still exists!