lim x->1 x^1/3-1 / x$1/4-1 , 极限 x趋向于1, x的三分一次方减去一除以 x的四分一次方减去一.._数学解答

lim x->1 x^1/3-1 / x$1/4-1 , 极限 x趋向于1, x的三分一次方减去一除以 x的四分一次方减去一.. 求解! 谢

人气：136 ℃　时间：2019-08-21 19:17:58

解答

x-1=[x^(1/3)-1][x^(2/3)+x^(1/3)+1]x-1=[x^(1/2)+1][x^(1/2)-1]=[x^(1/2)+1][x^(1/4)+1][x^(1/4)-1]原式=lim (x-1)/[x^(2/3)+x^(1/3)+1]×[x^(1/2)+1][x^(1/4)+1]/(x-1)x趋向于1=lim [x^(1/2)+1][x^(1/4)+1]/[x^(2/...