Evaluation of limit of the form `1^oo`

Find Lt_(x to oo)((3x^(2)+1)/(4x^(2)-1))^((x^(3))/(1+x)) Caution : The given limit is not of the form 1^(oo)

Evaluate the limit . Lt_( n to oo) (1+2^(4)+3^(4)+…….+n^(4))/(n^(5))

Evaluate the limit . Lt_(n to oo) sum_(i=1)^(n) (i)/(n^(2)+i^(2))

Evaluate the limit. lim_(n to oo) (sqrt(n+1)+sqrt(n+2)+……..+ sqrt(n+n))/(nsqrt(n))

Evaluate the limit: lim_(x rarr oo)((x+2)/(x+1))^(x+3)

The value of the limit lim _( n to oo) [(1)/(na) + (1)/( na +1) + (1)/( na +2) +.....+ (1)/( nb) ] is

Evaluate the limit: lim_(x rarr oo)[sqrt(a^(2)x^(2)+ax+1)-sqrt(a^(2)x^(2)+1)]

The value of the limit underset(x to oo)lim ((x^(2)-1)/(x^(2)+1))^(x^(2)) equal to

Evaluate the following limit : lim_(x rarr oo)(sqrt(x^2+x+1)- sqrt(x^2+1)) .