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 and . However, since it says prove it and then find it, how do i do that without an , proof?
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
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