a) 1/2; б) 5/2; c) 1
Пошаговое объяснение:
а) n->∞ lim n/2n+1=lim n/n(2+1/n)=lim 1/(2+1/n)=1/(2+1/∞) =1/(2+0)=1/2
б) n->∞ lim 5n-1/2n+1=lim (5-1/n)/(2+1/n)=(5-1/∞)/(2+1/∞)=(5-0)/(2+0)=5/2
в) n->∞ lim n^2-1/n^2+n+1=lim n^2(1-1/n^2)/n^2(1+1/n+1/n^2)=
= lim (1-1/n^2)/(1+1/n+1/n^2)=(1-1/∞^2)/(1+1/∞+1/∞^2)=(1-0)/(1+0+0)= =1/1=1
a) 1/2; б) 5/2; c) 1
Пошаговое объяснение:
а) n->∞ lim n/2n+1=lim n/n(2+1/n)=lim 1/(2+1/n)=1/(2+1/∞) =1/(2+0)=1/2
б) n->∞ lim 5n-1/2n+1=lim (5-1/n)/(2+1/n)=(5-1/∞)/(2+1/∞)=(5-0)/(2+0)=5/2
в) n->∞ lim n^2-1/n^2+n+1=lim n^2(1-1/n^2)/n^2(1+1/n+1/n^2)=
= lim (1-1/n^2)/(1+1/n+1/n^2)=(1-1/∞^2)/(1+1/∞+1/∞^2)=(1-0)/(1+0+0)= =1/1=1