`lim_(hrarr0)2((sqrt3Sin(h+pi/6)-Cos(h+pi/6))/(h(sqrt3Cosh-Sinh)))`

Evaluate: lim_(h rarr0)(2[sqrt(3)sin((pi)/(6)+h)-cos((pi)/(6)+h)])/(sqrt(3)h(sqrt(3)cos h-sin h))

"lim_(h rarr0)(sqrt(x+h)-sqrt(x))/(h)

lim_(h rarr0)((xsin x)(cosh-1))/h

sin(x-pi/6)+cos(x-pi/3)=sqrt3 sinx

lim_(x rarr pi/6)(sqrt(3)sin x-cos x)/(x-(pi)/(6))

lim_(h rarr0)(sin sqrt(x+h)-sin sqrt(x))/(h)=

lim_(h rarr0)(1)/(h)((1)/(sqrt(x+h))-(1)/(sqrt(x)))

lim_(theta rarr(pi)/(6))((sin(theta-(pi)/(6)))/(sqrt(3)-2cos theta)

(i) lim_(x to (pi)/(2)) (1+cos 2x)/((pi-2x)^(2)) (ii) lim_( x to 0) (1-cos x.sqrt(cos 2x))/(x^(2)) (iii) lim_(thetararr(pi)/(6)) (sin(theta-(pi)/(6)))/(sqrt(3)-2 cos theta)