求一题的极限
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求一题的极限
![](http://img.wesiedu.com/upload/3/89/3899ebf6548452334192c692a0d40552.jpg)
![](http://img.wesiedu.com/upload/3/89/3899ebf6548452334192c692a0d40552.jpg)
![求一题的极限](/uploads/image/z/17526995-35-5.jpg?t=%E6%B1%82%E4%B8%80%E9%A2%98%E7%9A%84%E6%9E%81%E9%99%90)
sin(arctan(sinx))是x的等价无穷小.
分子分母同时除以sin(arctan(sinx))
然后求出f(x)=(√xsin3x+x^2+arctan5x) / sin(arctan(sinx))的极限
lim f(x)= lim(√xsin3x+x^2+arctan5x) / sin(arctan(sinx))
=lim [√xsin3x / sin(arctan(sinx))] + lim [x^2 / sin(arctan(sinx))] + lim [arctan5x / sin(arctan(sinx))]
=lim(√x *3x/x)+lim(x^2/x)+lim(5x/x)
=0+0+5
=5
所以原极限=lim 1/f(x)=1/5
分子分母同时除以sin(arctan(sinx))
然后求出f(x)=(√xsin3x+x^2+arctan5x) / sin(arctan(sinx))的极限
lim f(x)= lim(√xsin3x+x^2+arctan5x) / sin(arctan(sinx))
=lim [√xsin3x / sin(arctan(sinx))] + lim [x^2 / sin(arctan(sinx))] + lim [arctan5x / sin(arctan(sinx))]
=lim(√x *3x/x)+lim(x^2/x)+lim(5x/x)
=0+0+5
=5
所以原极限=lim 1/f(x)=1/5