L = lim x->0 (1+√x•lnx)^(1/x) =
lim x-> 0 √x•ln x =
√x = t => x= t²
lim t->0 2tlnt = lim t->0 (2lnt)/(1/t) = (L'h) = (2/t)/(-1/t²) = (-2t²)/t = 0
L = lim x -> 0 (1+√x•lnx)^[1/(√x•lnx)•(√x•lnx /x)]
= e^lim x-> 0 (√x•lnx / x)
lim x-> 0 (√x•lnx / x) =
= lim x-> 0 (lnx / √x) =
√x = t => x = t² => t -> 0
= lim t -> 0 (ln(t²)/t) =
= lim t -> 0 (2lnt / t) =
ln t = y => t = e^y => y -> -∞
= lim y -> -∞ (2y/e^y) =
= lim y -> -∞ (2y/e^y) = (-∞/0+) = -∞•(1/0+) = -∞•∞ = -∞
L = e^(-∞) = 0
