Evaluate: `lim_(x->0)(1/(x^2)-1/(sin^2x))`

Evaluate: lim_(x->0)(e-(1+x)^(1/x))/x

Evaluate: ("lim")_(xvec0)(1^(1//sin^(2)x)+2^(1/(sin^(2)x)+....+n^(1//sin^(2)x)))^(sin^(2)x)

Evaluate lim_(xto0)(1-cos4x)/(x^(2))

Evaluate : lim_(xrarr0)(sin4x)/(sin2x)

Evaluate: lim_(x->2)(sin(e^(x-2)-1))/(log(x-1))

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

(a ) Evaluate : lim_(x to0) (sqrt(x^(2)+1)-1)/(sqrt(x^(2)+16)-4)

Evaluate lim_(xto-2)((1)/(x)+(1)/(2))/(x+2)

Evaluate (i) lim_(xto0)(sin3x)/(x) (ii) Find lim_(xto0)(sin3x)/(sin7x) (iii) Evaluate lim_(xto0)((sin3x+7x)/(3x+sin7x))