Evaluation of limit of the form `1^oo`

Evaluation OF limits || Some Illustrations based upon 0/0 form

Using the L .Hospital rule find limits of the following functions : lim_(x to oo) (e^(1//x^(2)-1))/(2"arc tan"x^(2)-pi)

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 limit: (lim)_(n rarr oo)((1^(2)-2^(2)+3^(3)-4^(2)+5^(2)+nterms)/(n^(2))

Evaluate the limit: (lim_(n rarr oo)cos(pi sqrt(n^(2)+n)) when n is an integer

Evaluate the following limits (if it exists) lim_(x rarr oo)(sqrt(x^(2)+1)-(x^(3)+1)^((1)/(3)))/((x^(4)+1)^((1)/(4))-(x^(5)+1)^((1)/(5)))

The value of limit lim_(t rarr oo)(int_(0)^(1)(tan^(-1)x)^(2)dx)/(sqrt(t^(2)+1))