Question

@wio.Prove only using the definition: lim as x->infinity of (1-x^2)/(x-2) =-infinity

Answer 1

First off I'm not sure i even have the right def for lim =-infinity

Answer 2

I think it is limf(x)=-infin. iff for all K>0, KeR, there exist an M>0 such that f(x)<-K provided x<=-M and x is in the domain of f

Answer 3

hmm.. using the definition? Divide both numerator and denominator by x^2

Answer 4

no, @smyers I need to prove using ONLY the definition.

Answer 5

I have (1-x^2)/x-2 <x-x^2/x-2x=x-1. if x>2

Answer 6

So I need to choose M=min(2, -k-1) I think but not sure

Answer 7

What do you think @agent0smith

Answer 8

Not familiar with this "definition" and it's hard to read what you wrote above since it's not easy to read that kinda math in plain text.

Answer 9

factorize by x at the top and at the bottom then simplify and then substitute and then you will find it is -infinity. no definition needed or you can use hospital theorem

Answer 10

I'm in analysis we can not use anything but the definition and algebra