# Thread: Prove that f has a limit

1. ## Prove that f has a limit

I just posted a similar problem, however this one states:

define f : (0,1) -> R by f(x)= ((9-x)^(1/2)-3)/x. Prove that f has a limit at 0 and find it.

This one also states to not use $\epsilon$ and $\delta$. However, since it says prove it and then find it, how do i do that without an $\epsilon$, $\delta$ proof?

2. Originally Posted by tn11631
I just posted a similar problem, however this one states:

define f : (0,1) -> R by f(x)= [tex]sqrt{x-9}[tex]-3/x. Prove that f has a limit at 0 and find it.

This one also states to not use $\epsilon$ and $\delta$. However, since it says prove it and then find it, how do i do that without an $\epsilon$, $\delta$ proof?
Hint: think derivatives (but I would guess that derivatives may not have been formalized yet)

3. Originally Posted by Drexel28
Hint: think derivatives (but I would guess that derivatives may not have been formalized yet)
sorry I had the problem a little messed up, I've fixed it. However, in class I don't think we've done any like that, or in fact the only ones we did were by using epsilon and delta and now were told not to.

4. Originally Posted by tn11631
sorry I had the problem a little messed up, I've fixed it. However, in class I don't think we've done any like that, or in fact the only ones we did were by using epsilon and delta and now were told not to.
Then I don't know what prove means

5. Originally Posted by Drexel28
Then I don't know what prove means
lol thats y I am confused. the other one I posted, they suggested to just factor the numerator and I guess plug in 1 normally, but again that problem said prove that f has a limit at 1. But thats kind of just showing it. But this time is says prove the limit exists and find it. so would I just go straight through since i can't use epsilon and delta? or is there another way to prove it

6. Originally Posted by Drexel28
Then I don't know what prove means
ah i think i've got it. . we have (9-x)^(1/2) -3/x and we mult both num and denom by (9-x)^(1/2) + 3 and we get 1/(9-x)^(1/2)+3 and 1 is a constant at each point and the denom at 0 has a limit of 6. therfore there is a theorem that says the limit exits and its 1/6...Guess I just needed a little discussion to get my brain to start lol