Evaluate: `("lim")_(nvecoo)(n^psin^2(n !))/(n+1)`

Evaluate lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.

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

Evaluate: lim_(x rarr oo)sin^(n)((2 pi n)/(3n+1)),n in N

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

Evaluate lim_(nto oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Evaluate :lim_(n rarr oo)sum_(r=1)^(n)(1)/((n^(2)+r^(2))^(1/2))

Evaluate: lim_(n rarr oo)n^(-n^(2)){(n+2^(0))n+2^(-1))(n+2^(-2))(n+2^(-n+1))}^(n)

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

Evaluate: lim_(nrarr0) (((2n)!)/(n!n^(n)))^(1/n)

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)