【f(x)二阶可导,g(x)=∫(0,1)f(xt)dt,且limx→0f(x)/x=A问g#39;(x)在x=0处是否连续】
<p>问题：【f(x)二阶可导,g(x)=∫(0,1)f(xt)dt,且limx→0f(x)/x=A问g#39;(x)在x=0处是否连续】<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">代巍巍的回答：<div class="content-b">网友采纳 g(x)=∫(0→1)ƒ(xt)dt 令u=xt,du=xdt t=0,u=0 t=1,u=x g(x)=(1/x)∫(0→x)ƒ(u)du g'(x)=(1/x)*ƒ(x)-(1/x²)∫(0→x)ƒ(u)du g'(0)=lim(x→0)ƒ(x)/x-lim(x→0)[∫(0→x)ƒ(u)du]/x² =A-lim(x→0)ƒ(x)/(2x) =A-(1/2)A =A/2 既然g'(0)存在,则g(x)=0处连续,可导则必定连续.
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