设函数f(x)在(-1,1)有定义且满足x≤f(x)≤x²+x证明f✀(0)存在且f✀(0)=1

2025-06-28 00:27:00
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证明:由已知,取x=0,得 0≤f(x)≤0 =>f(0)=0.由当x->0+时,1=lim x/x≤ limf(x)/x ≤ lim (x^2+x)/x=1=>limf(x)/x=1 (夹逼准则)由当x->0-时,1=lim (x^2+x)/x ≤ limf(x)/x ≤ lim x/x=1=>limf(x)/x=1 (夹逼准则)所以...