举报
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lim(x→0) [ sin(x^3) tanx / (1-cos(x^2)) ] 因为 在(x→0) 时, sin(x^3) 与 x^3 是等价无穷小, tanx 与 x 是等价无穷小,所以可以换一下 = lim(x→0) [ x^3 *x / (1-cos(x^2)) ] = lim(x→0) [ x^4 / (1-cos(x^2)) ] 在(x→0) 时,分子分母均→0,可以应用罗比达法则,分别求导 = lim(x→0) [ 4x^3 / (2 x*sin(x^2)) ] = lim(x→0) [ 2 x^2 / sin(x^2) ] = 2