lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?

问题描述:

lim(x趋向0)[1-cos(1-cos2x)]/x^4怎么解?

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

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