jak obliczyć tą granicę? pomocy: lim (2x+3/2x+1)^3x x−>∞

K. OWMH: lim [ (2x+3)/(2x+1)]^3x = lim [ (2x+1 +2)/(2x+1)]^3x =lim [ 1 + 2/(2x+1)]^3x= x→∞ x→∞ x→∞ lim [ 1 + /1(x+1/2)]^3x=lim [ 1 + 1/(x+1/2)]^{[3(x+1/2) − 3/2]}= x→∞ x→∞ (uwaga: x→∞ ⇒ (x+1/2)→∞ ) = lim ( [ 1 + 1/(x+1/2)]^(x+1/2) )³. lim [ 1 + 1/(x+1/2)]^−3/2= e³.1=e³ ( x + 1/2)→∞ x→∞