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

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]

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

lim_(n rarr oo)(3+sqrt(n))/(sqrt(n))

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

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

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

Let u_(n)=sum_(k=1)^(n)(k) and v_(n)=sum_(k=1)^(n)(k-0.5) . Then lim_(n rarr oo)(sqrt(u_(n))-sqrt(v_(n))) equals

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)2^(1/n)

lim_(n rarr oo) n(sqrt(n^(2)+8)-n) =