СРОЧНО
limx→∞((2x+1)/(x-1))^x

lim (x-1+x+2)/(x-1))^x =
lim (1 + (x+2)/(x-1))^x =
lim (1 + 1/[x-1/x+2])^[x-1/x+2] ^[x+2/x-1]*x =
exp ( lim [x+2/x-1]*x) = 
exp( lim (x^2 + 2x) / ( x - 1)) =
exp( lim (x + 2 )/ (1 -1/x)) =
exp( lim (x + 2 )) = +inf