Evaluate: `("lim")_(hvec0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(sqrt(3)cosh-sinh)`

Evaluate lim_(hto0) (2[sqrt(3)sin((pi)/(6)+h)-cos((pi)/(6)+h)])/(sqrt(3)h(sqrt(3)cosh-sinh)).

Evaluate lim_(hto0)(sqrt(x+h)-sqrt(x))/(h)

Evaluate (lim)_(hvec0)((a+h)^2sin^(-1)(a+h)-a^2sin^(-1)a)/h

Evaluate, lim_(xto(pi//6)) (sqrt(3)sinx-cosx)/(x-pi/6)

Evaluate the limit: ("lim")_(hvec0)[1/(h(8+h)^(1/3))-1/(2h)]

(lim)_(hvec0)((e+h)^(1n(e+h))-e)/hi s____

Evaluate lim_(x->pi)(sqrt(1-cos6x))/(sqrt2(pi/3-x))

Evaluate lim_(xto(pi)/(6)) (2-sqrt(3)cosx-sinx)/((6x-pi)^(2)).

Evaluate lim_(hto0) [(1)/(h^(3)sqrt(8+h))-(1)/(2h)].

A pair of tangents is drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60^0 . The area enclosed by these tangents and the arc of the circle is (a) 2/(sqrt(3))-pi/6 (b) sqrt(3)-pi/3 (c) pi/3-(sqrt(3))/6 (d) sqrt(3)(1-pi/6)