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

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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
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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
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

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
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^(2/3)+x^(1/3)+1]
x趋向于1
=(1+1)(1+1)/(1+1+1)=4/3

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→1
=lim [x^(1/2)+1][x^(1/4)+1]/[x^(2/3)+x^(1/3)+1]
x→1
=(1+1)(1+1)/(1+1+1)=4/3

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