Question

lim n→+∞(√(n^2+3n)-√(n^2+1))=

даю 35 баллов

Answer 1

Lim n→+∞(√(n^2+3n)-√(n^2+1)) =  Lim n→+∞(√(n^2+3n)-√(n^2+1))*(√(n^2+3n)+√(n^2+1))/(√(n^2+3n)+√(n^2+1)) = Lim n→+∞(n^2+3n - n^2 - 1)*/(√(n^2+3n)-√(n^2+1)) = { делим на n} = Lim n→+∞(3n/n-1/n)*/ (√(n^2/n^2+3n/n^2)-√(n^2/n^2+1/n^2)) = (3 - 0)/(√(1 + 0) + √(1 + 0)) = 3/2