Question

I have a stupid limit question: if f(t)=(t+1)/(2t+3), then the limit of f as t approaches infinity is 1/2, correct? but the limit of f as t approaches zero is 1/3. Would it be fair to say that this is because as we approach infinity the t-terms overpower the constant terms, while as t approaches 0, the constant terms overpower the t-terms? If that's not completely wrong, is there a better way to explain it?

Answer 1

Sure, you can say it that way

Answer 2

is there a better explanation? or is that pretty much it.

Answer 3

Depends on how rigorous you want to get. Have you covered the calculus 1 sequence already

Answer 4

I did it a long time ago, and am struggling to remember the intuitions of why certain computations work.

Answer 5

Well, for this example it's fairly trivial because the limit is in a convenient (or "simplest") form. You're essentially using the proof that the limit as x approaches infinity of 1/x is 0, or you can use the graph of the function by determining the domain/range and seeing at which points the graph goes wacky (asymptotes), etc. There's different ways to go about it

Answer 6

yeah, I was trying to use a simple example to get at the underlying concept. Is it mostly a matter of simplifying the function into a form where I can compare rates of change then? so 1/x goes to 0 because x obviously grows much faster than a constant?

Answer 7

That's the idea of limits, yes

Answer 8

ok, I will chew on that. thanks so much for your help.