求极限lim(x→0）（根号下1+tanx减去根号下1+sinx）/sin^3x
郑雨威刷粉282
分子分母同时乘以(根号下1+tanx加根号下1+sinx）,则所求＝lim(x→0）（tanx-sinx）/[sin^3x（根号下1+tanx加根号下1+sinx）]＝lim(x→0）（tanx-sinx）/(2sin^3x),分子分母除以sinx=lim(x→0）（1/cosx-1)(2sin^2x)=lim(x→0）（1-cosx)/(2sin^2x)用洛比达法则,分子分母同时求导＝lim(x→0）sinx/(4sinx cosx)=lim(x→0）1/(4cosx)=1/4
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扫描下载二维码lim(1+tanx/1+sinx)^1/sinx x趋近于0
原式=lim(x->0){[1+(tanx-sinx)/(1+sinx)]^[((1+sinx)/(tanx-sinx))*((tanx-sinx)/(sinx+sin²x))]}=e^{lim(x->0)[(tanx-sinx)/(sinx+sin²x)]} (应用重要极限lim(z->0)[(1+z)^(1/z)]=e)=e^{lim(x->0)[(1/co...
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