lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?

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lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?
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lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?
lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?

lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?
用等价无穷小lim(x趋向0)[1-cosx]等价于lim(x趋向0)[(x^2)/2]
lim(x趋向0)[1-cos(1-cos2x)]/x^4=lim(x趋向0)[1-cos(2x^2)]/x^4=lim(x趋向0)[1-cos(2x^2)]/x^4
=lim(x趋向0)[(4x^4)/x^4]=4

lim(x趋向0)[1-cos(2x^2)]/x^4=lim(x趋向0)[1-cos(2sinx^4)]/x^4
=lim(x趋向0)[(2x^4)/x^4]=2