作业帮高数极限题求详解,求x趋正无穷时 ,x^(1/2) [x^(1/x)-1] 极限.
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高数极限题求详解,
求x趋正无穷时 ,x^(1/2) [x^(1/x)-1] 极限.
求x趋正无穷时 ,x^(1/2) [x^(1/x)-1] 极限.
lim x^(1/2) [x^(1/x)-1]=lim [x^(1/x)-1]/[x^(-1/2)]= lim [x^(1/x)-1]'/[x^(-1/2)]'
=lim x^(1/x)*(1-logx)/x^2/[-0.5*x^(-1.5)]
=lim x^(1/x)* lim (1-logx)/x^2/[-0.5*x^(-1.5)]
=1*0=0
再问： 请问lim (1-logx)/x^2/[-0.5*x^(-1.5)] =0 是怎么得出的呢 ？ 抱歉没太看懂……
再答： (1-logx)/x^2/[-0.5*x^(-1.5)](化简) =2(logx-1)/x^0.5 而lim(logx-1)/x^0.5 =limlog(x)/x^0.5-lim1/x^0.5 =lim[log(x)]'/[x^0.5]'-0 =lim[1/x]/[0.5x^(-0.5)] =lim2*1/x^0.5 =0
=lim x^(1/x)*(1-logx)/x^2/[-0.5*x^(-1.5)]
=lim x^(1/x)* lim (1-logx)/x^2/[-0.5*x^(-1.5)]
=1*0=0
再问： 请问lim (1-logx)/x^2/[-0.5*x^(-1.5)] =0 是怎么得出的呢 ？ 抱歉没太看懂……
再答： (1-logx)/x^2/[-0.5*x^(-1.5)](化简) =2(logx-1)/x^0.5 而lim(logx-1)/x^0.5 =limlog(x)/x^0.5-lim1/x^0.5 =lim[log(x)]'/[x^0.5]'-0 =lim[1/x]/[0.5x^(-0.5)] =lim2*1/x^0.5 =0
高数极限题求详解,求x趋正无穷时 ,x^(1/2) [x^(1/x)-1] 极限.
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