求極限 lim(2x-1/2x+1 )^x+1 x趨向于無窮,求這個(gè)極限,

數(shù)學(xué)人氣：525 ℃時(shí)間：2020-01-26 05:38:11

優(yōu)質(zhì)解答

lim [x→∞] [(2x-1)/(2x+1)]^(x+1)
=lim [x→∞] [1-2/(2x+1)]^(x+1)
=lim [x→∞] [1-2/(2x+1)]^{[(2x+1)/2](x+1)[2/(2x+1)]}
=lim [x→∞] {[1-2/(2x+1)]^[-(2x+1)/2]}^{(x+1)[2/(2x+1)]}
=lim [x→∞] {[1-2/(2x+1)]^[-(2x+1)/2]}^lim[x→∞]{(x+1)[2/(2x+1)]}這里有點(diǎn)問題,漏了負(fù)號(hào)
應(yīng)該是=lim [x→∞] {[1-2/(2x+1)]^[-(2x+1)/2]}^lim[x→∞]{-(x+1)[2/(2x+1)]}
=e^lim[x→∞][-(2x+2)/(2x+1)]
=e^(-1)