`Lt_(x->0 )(-1+sqrt(("tanx-sinx)+sqrt((tanx-sinx)+sqrt(..........)))oo)/(-1+sqrt(x^3+sqrt(x^3+sqrt(x^3+....)))oo`

The value of lim_(xto0^(+))(-1+sqrt((tanx-sinx)+sqrt((tanx-sinx)+sqrt((tanx-sinx)+…oo))))/(-1+sqrt(x^(3)+sqrt(x^(3)+sqrt(x^(3)+…oo)))) is

Solve : sqrt(tanx+sinx)+sqrt(tanx-sinx)=2cosxsqrttanx

lim_(xto0)(sqrt(1+sinx)-sqrt(1-sinx))/tanx

lim_(x->oo)x^(3/2)(sqrt(x^3+1)-sqrt(x^3-1))

Evaluate: (a) sqrt((x^(3))sqrt( y sqrt(x^(3)sqrt(y....oo)))) ,

Lim_(x rarr 0)(tanx sqrt (tanx)-sin x sqrt(sinx))/(x^(3).sqrtx) equals

tan^(2)x -(1+sqrt(3))tanx + sqrt(3)=0