已知lim(x→0)[sin6x–f(x)tanx]/x=0,求lim(x→0)[6-f(x)]/x

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已知lim(x→0)[sin6x–f(x)tanx]/x=0,求lim(x→0)[6-f(x)]/x

已知lim(x→0)[sin6x–f(x)tanx]/x=0,求lim(x→0)[6-f(x)]/x
已知lim(x→0)[sin6x–f(x)tanx]/x=0,求lim(x→0)[6-f(x)]/x

已知lim(x→0)[sin6x–f(x)tanx]/x=0,求lim(x→0)[6-f(x)]/x
x趋近0时,sinx与x、tanx与x都是等价无穷小
即,lim(x->0)(sinx/x)=1
lim(x->0)(tanx/x)=1
limx趋近于0[6sinx-(tanx)f(x)]/x³
=limx趋近于0[6-f(x)]/x²
=0
所以,limx趋近于0[6-f(x)]/x²=0

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