1 a
lim f(x) =lim [e^(-x)]/(1-x) = lim 1/([e^(-x)](1-x)) =0 daca x->+infinit
=>y=0 asimtota orizontala spre +infinit

ex 1b)va rog [color=blue][/color]

1 b
lim f(x) =lim [e^(-x)]/(x+1) = lim 1/([e^(-x)](x+1)) =0 daca x->-infinit
=>y=0 asimtota orizontala spre -infinit

ex 2 c..variantele noi?

2c
1<lnx<2 pentru orice x apartine [e,2^2]
1<(lnx)^n<2^n se imparte relatia la x sensul nu se schimba
1/x<[(lnx)^n]/<(2^n)/x integram de la e la e^2
I0<In<(2^n)I0
I0=1 de la punctul a
1<In<2^n

In=int [(lnx)^n]/x dx de la e la e^2
substitutie y=lnx =>dy=1/x dx
daca x=e =>y=lne=1
daca x=e^2 =>y=ln(e^2)=2
In=int y^n de la 1..2 =[y^(n+1)]/(n+1) bara 1..2 =[2^(n+1) -1]/(n+1)
=>1<[2^(n+1) -1]/(n+1)< 2^n pentru orice n natural