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3n^(2)-2sqrt(6)n+2=0...

3n^(2)-2sqrt(6)n+2=0

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

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

lim_(n rarr oo)(1)/(n^(3))(sqrt(n^(2)+1)+2sqrt(n^(2)+2^(2))+...+n sqrt(n^(2)+n^(2))) is equal to

lim _(x to oo) (1)/(n ^(3))(sqrt(n ^(2)+1)+2 sqrt(n ^(2) +2 ^(2))+ .... + n sqrt((n ^(2) + n ^(2)))=:

lim _(x to oo) (1)/(n ^(3))(sqrt(n ^(2)+1)+2 sqrt(n ^(2) +2 ^(2))+ .... + n sqrt((n ^(2) + n ^(2)))=:

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 rarr0)(sqrt(1+n^(2))-sqrt(1-n+n^(2)))/(3^(n)-1)

{:(" "Lt),(n rarr oo):} [(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+(sqrt(n^(2)-3^(2)))/(n^(2)).+....n "terms"]=