极限一题,
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极限一题,
极限一题,
极限一题,
因为 极限有数值 说明
x+f(x)与 x^3 是等价的
必然有 x+f(x)|(x=0) =0
∴ f(0)=0
lim(x-0) [x+f(x)]/x^3 罗比塔法则有
= lim(x-0) [1+f'(x)]/3x^2 此时 应有1+f'(x)|(x=0)=0 ∴ f'(0) =-1
=lim(x-0) [f"(x)]/6x 此时 应有f"(x)|(x=0)=0 ∴ f"(0) =0
=lim(x-0) f'''(x) /6 =-1
∴f'''(0) =-6
带入lim(x-0) f(x)/x 属于0/0 罗比塔有
=lim(x-0) f'(x) = -1