Question

Lim n->бесконечности 2n^2/n^2+n+1

Answer 1

Lim n->∞ 2n^2/(n^2+n+1) =  Lim n->∞ 2n^2/(n^2+n+1) =   Lim n->∞ 2n^2/n^2/(n^2/n^2+n/n^2+1/n^2) = 2/(1+0+0) = 2  

делим на n^2

Answer 2

To find the limit of the expression as n approaches infinity, we can simplify the expression first:

lim(n -> ∞) 2n^2 / (n^2 + n + 1)

As n approaches infinity, the higher order terms dominate the expression. In this case, the term with the highest power of n is n^2. So, we can neglect the lower order terms (n and 1) in the denominator:

lim(n -> ∞) 2n^2 / n^2

Now, we can cancel out the common factor of n^2:

lim(n -> ∞) 2

Thus, the limit of the expression as n approaches infinity is 2.