Question

Happy holidays guys!
As a gift, I'll leave you a quite interesting exercise.
I did it myself and I found it very interesting:

Answer 1

prove:
\[I) \lim_{x \rightarrow 0} \frac{ \ln (f(x)+1) }{ f(x) }=1\]
II) H) f is continuos in the interval [a,b]
f(a).f(b)<0

T) there exists an element c such that f(c)=0

Answer 2

Actually, it's not difficult to see why it holds.
Nonetheless, nice job.

Answer 3

throw a medat at him