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(1-cos3x)/(1-cos4x)当x-->0时的极限是多少?
题目详情
(1-cos3x)/(1-cos4x)当x-->0时的极限是多少?
▼优质解答
答案和解析
应用洛必达法则分子分母同时对x求导,得3sin(3x)/4sin(4x),又知x－－>0时,sin(3x)->3x;sin(4x)->4x;得最后答案为9/16
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修改如下:运用倍角公式展开分子分母,得:2(sin(1.5x))^2/2(sin(2x))^2=(sin(1.5x)/sin(2x))^2;x->0时,该式得:9/16
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修改如下:运用倍角公式展开分子分母,得:2(sin(1.5x))^2/2(sin(2x))^2=(sin(1.5x)/sin(2x))^2;x->0时,该式得:9/16
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