求极限 求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值
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![求极限 求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值](/uploads/image/z/2535257-65-7.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90+%E6%B1%82%28tanx-x%29%2F%28x%5E2%2Atanx%29%E5%BD%93x%E8%B6%8B%E5%90%910%E6%97%B6%E5%80%99%E7%9A%84%E6%9E%81%E9%99%90%E5%80%BC%E6%B1%82%28tanx-x%29%2F%28x%5E2%2Atanx%29%E5%BD%93x%E8%B6%8B%E5%90%910%E6%97%B6%E5%80%99%E7%9A%84%E6%9E%81%E9%99%90%E5%80%BC)
求极限 求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值
求极限 求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值
求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值
求极限 求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值求(tanx-x)/(x^2*tanx)当x趋向0时候的极限值
lim(tanx-x)/(x^2tanx)=
lim[(sinx/cosx)-x]/(x^2sinx/cosx)=
lim(sinx-x*cosx)/(x^2*sinx)【此步为上下同乘以cosx后所得】=
lim(sinx-x*cosx)/(x^3)【此步为利用x趋于0时,sinx和x等价无穷小】=
lim(cosx-cosx+x*sinx)/(3x^2)【此步为利用洛比达法则上下求导】=
lim(x*x)/(3x^2)【利用x趋于0时,sinx和x等价无穷小】=
1/3
lim(x->0)(tanx-x)/(x^2*tanx)
= lim(x->0)(tanx-x)/(x^2*x)*[x/tanx]
= lim(x->0)(tanx-x)/(x^3)
= lim(x->0)[(secx)^2-1]/(3x^2)
= 3lim(x->0)(tanx)^2/(x^2)
= 3
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lim(x->0)[tanx/x] = 1