Find `(dr)/(dn)` , `r=n^(sqrt(n))`

int(n)/(sqrt(n-3))dn

lim_ (n rarr oo) sum_ (n = 1) ^ (n) (sqrt (n)) / (sqrt (r) (3sqrt (r) + 4sqrt (n)) ^ (2))

Find underset( n rarr oo) ("lim") (sqrt( n^(2) + 1)+ sqrt( n ) )/( sqrt( n ^(2) + 1)- sqrt( n ) )

If sum_(r=1)^(n)T_(r)=n(2n^(2)+9n+13), then find the sum sum_(r=1)^(n)sqrt(T_(r))

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to tan^(-1)(sqrt(n))-(pi)/(4)tan^(-1)(sqrt(n+1))-(pi)/(4)tan^(-1)(sqrt(n))(d)tan^(-1)(sqrt(n)+1)

The value of sum_(k=2)^(oo){Lt_(n rarr oo)sum_(r=1)^(n)((sqrt(n))/(sqrt(r)(k sqrt(n)-sqrt(r))^(2))}]}

When n = 5 and r = 2, find the values of : (i) (n!)/(r!) (ii) (n!)/(r!(n-r)!)

Evaluate : lim_(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2)(3sqrt(2)+4sqrt(n))^(2))+(sqrt(n))/(sqrt(3)(3sqrt(3)+4sqrt(n))^(2))+.......+(1)/(49n)]