meili 发表于 2022-10-27 15:18:37

f(x)有二阶连续导数大于0F(0)=F#39;(0)=0u是f(x)在(x,f(x))处切线在x轴截距,求lim(x→0)xf(u)/uf(x)

<p>问题:f(x)有二阶连续导数大于0F(0)=F#39;(0)=0u是f(x)在(x,f(x))处切线在x轴截距,求lim(x→0)xf(u)/uf(x)
<p>答案:↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">彭宏韬的回答:<div class="content-b">网友采纳  由题可知,f(x)=ax²+o(x²)  u=x-f(x)/f'(x)  limu/x=lim  而limf(x)/xf'(x)=limf'(x)/=limf''(x)/=f''(0)/(2f''(0)+0)=1/2,所以limu/x=1/2  且limf(u)/f(x)=lim/=limu²/x²=1/4  所以原式=/(limu/x)=1/2
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