Quote by naspek
1. The problem statement, all variables and given/known data
lim.......... (1 + 1/n^2)(7/n+1)
n>infinity
3. The attempt at a solution
lim.......... (1 + 1/n^2)(7/n+1)
n>infinity
= (7/n + 1) + (7/n^3 + n^2)
bring out 7 because constant..
7lim.......... (1/n + 1) + (1/n^3 + n^2)
n>infinity
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7lim.......... (n^2 + n + 1) / (n^3 + 2n^2 +n)
n>infinity
limit does not exist.. am i correct?

No. Don't multiply the two factors. Each one has a limit that is readily obtainable. As n gets large without bound, what happens to 1/n
^{2}? What happens to 1 + 1/n
^{2}? What happens to 7/n? What happens to 7/n + 1?
The limit
does exist.