`lim_(x->0^+) (-1+sqrt(1+4(tanx-sinx)))/(-1+sqrt(1+4x^3))`

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

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

lim_(x->0)(e^(x)-1)/(sqrt(4+x)-2) =

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

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

lim_(x rarr0)(sqrt(1+x^(2))-sqrt(1+x))/(sqrt(1+x^(3))-sqrt(1+x))