lim_(n rarr oo)(sqrt(n^(3)-2n^(2)+1)+root(3)(n^(4)+1))/(root(4)(n^(6)+6n^(5)+2)-root(5)(n^(7)+3n^(3)+1)),n in N

lim_(n rarr oo)(sqrt(n^(3)-2n^(2)+1)+3sqrt(n^(4)+1)3)/(4sqrt(n^(6)+6n^(5) )+2)-5sqrt(n^(7)+3n^(3)+1))

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)

lim_ (n rarr oo) [(sqrt (n ^ (2) +1) + sqrt (n)) / (root (4) (n ^ (3) + n) -root (4) (n))]

lim_(n rarr oo)((n^(3)-2n^(2)+1)^((1)/(2))+(n^(4)+1)^((1)/(3 ))))/((n^(6)+6n^(5)+2)^((1)/(4))-(n^(7)+3n^(2)+1)^((1 )/(5)))

lim_(n rarr oo)((4+3n+n^(6))^((1)/(3)))/(1+3n+2n^(2))

The value of lim_(n rarr oo)(sqrt(3n^(2)-1)-sqrt(2n^(2)-1))/(4n+3) is

lim_(n rarr oo)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

lim_ (n rarr oo) ((sqrt (n ^ (2) +1) + n) ^ (2)) / ((n ^ (6) +1) ^ (1/3))

lim_(n rarr oo)(5^(n+1)+3^(n)-2^(2n))/(5^(n)+2^(n)+3^(2n+3))