cos3x除以x三次方的极限

投稿:清明雨揽月 优质问答领域创作者 发布时间:2023-10-04 15:42:05
cos3x除以x三次方的极限

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这个题要用洛必达法则,上下求导,需要知道cos3x等价无穷小是多少,x^3求导是3星^2,再看题目是趋向于∞还是0,再进行下一步计算

cos3x除以x三次方的极限

(x→0)lim{(1-cosx)/x³}

= (x→0)lim{[1-1+2sin²(x/2)]/x³}

= (x→0)lim{2sin²(x/2)]/8*(x/2)³}

= (x→0)lim{sin²(x/2)]/4*(x/2)³}

= (x→0)lim{(x/2)²]/4*(x/2)³}

= +∞

(x→0)lim{(1-cosx)/x³}

= (x→0)lim{[1-1+2sin²(x/2)]/x³}

= (x→0)lim{2sin²(x/2)]/8*(x/2)³}

= (x→0)lim{sin²(x/2)]/4*(x/2)³}

= (x→0)lim{(x/2)²]/4*(x/2)³}

= +∞

(x→0)lim{(1-cosx)/x³}

= (x→0)lim{[1-1+2sin²(x/2)]/x³}

= (x→0)lim{2sin²(x/2)]/8*(x/2)³}

= (x→0)lim{sin²(x/2)]/4*(x/2)³}

= (x→0)lim{(x/2)²]/4*(x/2)³}

= +∞