`lim_(n rarr1)(n^(2)-sqrt(n))/(sqrt(n)-1)`

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

lim_(n rarr4)(sqrt(2n+1)-3)/(sqrt(n-1)-sqrt(2))

If f(x) is continuous in [0,1] and f((1)/(2))=1 prove that lim_(n rarr oo)f((sqrt(n))/(2sqrt(n+1)))=1

lim_(n rarr oo)(sqrt(n+1)-sqrt(n))=0

lim_(n rarr oo) sqrt(n)/sqrt(n+1)=

lim_(n rarr oo)(1)/(sqrt(n)sqrt(n+1))+(1)/(sqrt(n)sqrt(n+2))+......+(1)/(sqrt(n)sqrt(4n))

If nEN and a_(n)=2^(2)+4^(2)+6^(2)+....+(2n)^(2) and b=1^(2)+3^(2)+5^(2)+...(2n-1)^(2). Find the value lim_(n rarr oo)((sqrt(a_(n))-sqrt(b_(n)))/(sqrt(n)))

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

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

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