meili 发表于 2022-10-27 15:18:14

设f(x)具有连续的二阶可导,且f(0)二阶导=4,lim(x-gt;0)f(x)/x=0,则lim(x-gt;0)(1+f(x)/x)^1/x=?

<p>问题:设f(x)具有连续的二阶可导,且f(0)二阶导=4,lim(x-gt;0)f(x)/x=0,则lim(x-gt;0)(1+f(x)/x)^1/x=?
<p>答案:↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">田干的回答:<div class="content-b">网友采纳  lim(x->0)f(x)/x=0,所以f(x)=0lim(x->0)f(x)/x=lim(x->0)f'(x)=0,所以f'(x)=0设L=lim(x->0)(1+f(x)/x)^1/xln(L)=lim(x->0)ln(1+f(x)/x)/x=lim/=lim(x->0)f''(x)/=...
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查看完整版本: 设f(x)具有连续的二阶可导,且f(0)二阶导=4,lim(x-gt;0)f(x)/x=0,则lim(x-gt;0)(1+f(x)/x)^1/x=?