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](/uploads/image/z/117501-69-1.jpg?t=%E5%B7%B2%E7%9F%A5lim%28x%E2%86%920%29%5Bsin6x%E2%80%93f%28x%29tanx%5D%2Fx%3D0%2C%E6%B1%82lim%28x%E2%86%920%29%5B6-f%28x%29%5D%2Fx)
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
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
已知lim(x→0)[sin6x–f(x)tanx]/x=0,求lim(x→0)[6-f(x)]/x
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