Evaluate :

`lim_( n -> oo ) x^n / ( x^n + 1 )`

Evaluate lim_ (n rarr oo) n ^ (2) int _ (- (1) / (2)) ^ ((1) / (pi)) (2006sin x + 2007cos x) | x | dx

Evaluate: lim_(x rarr oo) [(4x^(n)+1)/(5x^(n)+5)] .

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

lim_ (n rarr oo) (x ^ (n)) / (n!)

Evaluate lim_ (n rarr oo) [(1+ (1) / (n)) 91+ (2) / (n)) .... (1+ (n) / (n))] ^ ((1) /(a))

Evaluate: lim_ (n rarr oo) (1 * 2 + 2 * 3 + 3 * 4 + ... + n (n + 1)) / (n ^ (3))

evaluate lim_ (n rarr oo) ((e ^ (n)) / (pi)) ^ ((1) / (n))

lim_ (n rarr oo) (1) / (1 + x ^ (n))

Evaluate: (lim)_(n rarr oo)[(n!)/(n^(n))]^(1/n)