求一题的极限
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求一题的极限
求一题的极限
求一题的极限
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