Question

Limita de la ex 8 in functie de parametrul a.

Answer 1

Pt a=3  limita   e   1
a=/=3
se   da a^n  factor   comun   fortat
lim a^n(2^n/a^n+1)/3^n(2^n/3^n+1)=lim(a/3)^n*{(2^n/a^n+1)/(2^n/3^n+1)}
PT a>3 {...}→1
lim(a/3)^n→∞=>L=+∞
___________________
Pt a∈(1.3)   {...}→1
lim(a/3)^n=0   L→0
Caz  a∈(0,1)
Se   da    la   numarator 2^n factor   comun  la    numarator   si   3^n   la   numitor

lim(2/3)^n*(1+(a/2)^n)/((2/3)^n+1)=0*1=0