i originally posted this in the analasys section. Since i haven't been getting any results, I've figured that perhaps people feel it should be in the homework section. anyway, I am trying to prove the folloting:
if lim f(x)= infinity= lim g(x)
x->infinity x->infinty
and lim...
i also have the following hints to use after the hints in the original post:
fix a>k, then by cauchy mvt,
f(x)-f(a) f'(c)
_______ = ____ > m(4/3) for x>a>k*, and such that
g(x)-g(a) g'(c)
g(x)>g(a)>0 and f(x)> f(a)> 0 where c>a>k*
i just realized that my post is quite confusing. i suppose I am not too sure what to ask. If you don't understand my original post, perhaps u can just help me start off the proof. thanks.
if lim f(x)= infinity= lim g(x)
x->infinity x->infinty
and lim f'(x)/g'(x)=infinity
x-> infinity
then lim f(x)/g(x)=inifity
x-> inifinity
The above fact is what I am trying to prove. From my notes, i see the following:
For m>0, choose k>0, such that if...