神马作文网高数极限题求详解,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.
![高数极限题求详解,求x趋正无穷时 ,x^(1/2) [x^(1/x)-1] 极限.](/uploads/image/z/7430628-12-8.jpg?t=%E9%AB%98%E6%95%B0%E6%9E%81%E9%99%90%E9%A2%98%E6%B1%82%E8%AF%A6%E8%A7%A3%2C%E6%B1%82x%E8%B6%8B%E6%AD%A3%E6%97%A0%E7%A9%B7%E6%97%B6+%2Cx%5E%281%2F2%29+%5Bx%5E%281%2Fx%29-1%5D+%E6%9E%81%E9%99%90.)
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
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