Proving limit equivalence statements.

[cookiesyum]

Homework Statement

Is it always true that

lim f(x) _x-->infinity = lim f(1/t)_{t --> 0}

lim f(x)_{x--> 0} = lim f(1/n)_n-->infinity

The Attempt at a Solution

How can you begin to prove or disprove these statements if you don't know what f is doing to x. In other words, lim f(x) could not exist or it could depending on what f(x) is doing to the x's right? So from where do I start?

 

[lanedance]

not too sure on this one, but as some ideas, consider the 2nd case
lim x->0, f(x)

for the limit to exist, the limit must be same for the approach to zero form both sides
lim x->0+, f(x) = lim x->0-, f(x)

it seems to me changing to the case, lim n-> inf, f(1/n) only really consider the 0+ approach

consider a step function at the origin

however that will only be a problem if the limit does not exist, if the limit does exist then i think you might be ok - however it might be some food for though for the first case what if t approaches 0-, then would you require the negative infinite limit to be the same as the positive one?