Question

Ajutați.ma si pe mine la limita asta..va rog mult!!

Answer 1

Răspuns:

Explicație pas cu pas:

(n+2)^4 - n^4 = (n+2)^2 * (n+2)^2 - n^4 = (n^2 + 4n + 4)(n^2 + 4n + 4) - n^4 =

n^4 + 4n^3 + 4n^2 + 4n^3 + 16n^2 + 16n + 4n^2 + 16n + 16 - n^4 =

8n^3 + 24n^2 + 32n + 16

(n+2)^3 + n^3 = (n+2)^2 * (n+2) + n^3 = (n^2 + 4n + 4 ) (n+2) + n^3 = n^3 +2n^2 + 4n^2 + 8n + 4n + 4 + n^3 = 2n^3 + 6n^2 + 12 n + 4

lim n -> inf (8n^3 + 24n^2 + 32n + 16)/(2n^3 + 6n^2 + 12 n + 4 ) = 8/2 = 4