Question

(arctanx-sinx)/x*x*x的x趋于0时的极限

Answer 1

过程省去limx-->0

(arctanx-sinx)/x*x*x

=[1/(1+x²)-cosx]/3x²(洛必达法则)

=[1-x²-1+2sin²(x/2)]/3x² (1/(1+x²)展开,cosx=1-2sin²x/2)

=(-x²+2*x²/4)/3x² (sinx/2和x/2为等价无穷小)

=(-1/2)/3

=-1/6

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