Question

Va rog , cum se rezolva aceasta limita ? Si care este rezultatul...

Answer 1

lim x->ꝏ √(x+√x) - √x = ?

√x = t => x = t²

x -> ꝏ => t -> inf

=> lim t -> ꝏ √(t²+t) - t =

= lim t -> ꝏ (√(t²+t) - t)(√(t²+t) + t)/(√(t²+t) +t) =

= lim t -> ꝏ (t²+t - t²)/(√(t²(1+1/t))+t) =

= lim t -> ꝏ t/(t√(1+1/t)+t) =

= lim t -> ꝏ t/(t(√(1+1/t)+1) =

= lim t -> ꝏ 1/(√(1+1/t)+1)

= 1/2