ok

not ok3. if lim x->infinity f(x) = +infinity, then for any k (all real numbers), lim x->+infinity k/f(x) = 0 -- False

why do you say it's false ?

the exponential grows faster than any power of x, which grows faster than the logarithm.2. There is a natural number n such that the power function f(x)=x^n is growing faster than the exponential function g(x)=e^x -- True

4. The function f(x) = lnx grows more slowly than any positive power of x -- True