meili 发表于 2022-10-27 15:26:28

设函数g(x)={f(x)/x,x≠0;a,x=0},f(x)具有二阶连续导数,且f(0)=0,(1)求a为何值时,g(x)在x=1处连续;(2)求g#39;(0).

<p>问题:设函数g(x)={f(x)/x,x≠0;a,x=0},f(x)具有二阶连续导数,且f(0)=0,(1)求a为何值时,g(x)在x=1处连续;(2)求g#39;(0).
<p>答案:↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">彭晓的回答:<div class="content-b">网友采纳  (1)a=g(0)=lim(x→0)g(x)=lim(x→0)f(x)/x=lim(x→0)f'(x)=f'(0)(2)g'(0)=lim(x→0)(g(x)-g(0))/(x-0)=lim(x→0)(f(x)/x-f'(0))/x=lim(x→0)(f(x)-f'(0)x)/x^2=lim(x→0)(f'(x)-f'(0))/(2x)=1/2lim(x→0)f''(x)=1/2f...
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