Evaluate :
`lim_( x -> oo ) 1/2`

Evaluate : lim_( x -> oo ) 2^x Sin( a/2^x )

Evaluate: lim_(x rarr oo)[(x-1)/(x-2)]^x

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

Evaluate: lim_(x rarr oo)[(1^3+2^3+3^3+...........+x^3)/x^4]

Evaluate: lim_ (x rarr oo) ((1 + 5x ^ (2)) / (1 + 3x ^ (2))) ^ (- x ^ (2))

Evaluate: lim_(x rarr oo)[x(a^((1)/(x))-1)],a>1

Evaluate: lim_(x rarr oo)x^((1)/(x))

Evaluate: lim_(x rarr oo) [(x^(2)+x+6)/(x+1)] .

Evaluate: (lim)_(x rarr oo)(1+(1)/(x))^(x)

Evaluate lim_(x rarr oo)[(x+1)^((x+2)/(x+1))-x^((x+1)/(x))]