Evaluate: `("lim")_(nvec0)(1^1//sin^(2x)+2^1/(sin^(2x))++n^1//sin^(2x))^sin^(2x)`

Evaluate lim_(xto0) {1^(1//sin^(2)x)+2^(1//sin^(2)x)+...+n^(1//sin^(2)x)}^(sin^(2)x) .

Evaluate: (lim)_(x->0)(e^x-1-x^3)/(sin^6 2x)

The value of lim_(xrarr0) {1^((1)/(sin^(2)x)+)2^((1)/(sin^(2)x))+3^((1)/(sin^(2)x))+.....+n^((1)/sin^(2)x)}^(sin^2x) , is

Evaluate: lim_(x rarr0)(1)/(x)sin^(-1)((2x)/(1+x^(2)))

Evaluate: lim_(x rarr0)((1)/(x^(2))-(1)/(sin^(2)x))

lim_(x->0)[1^(1/sin^2x)+2^(1/sin^2x)+...................+n^(1/sin^2x)]^(sin^2x) =

Evaluate: lim_(n rarr0)(e^(sin x)-(1+sin x))/({tan^(-1)(sin x)}^(2))

Evaluate : lim_(x to 0)(1-cosxcos2xcos3x)/(sin^(2)2x)

Evaluate lim_(x rarr0)(2sin x-sin(2x))/(x^(3))