极限问题(急)第一题:lim的x趋近于无穷大(x-1)/(x+1)的x次方第二题:lim的x趋近于1 1/(x-1)减去
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极限问题(急)
第一题:lim的x趋近于无穷大(x-1)/(x+1)的x次方
第二题:lim的x趋近于1 1/(x-1)减去2/(x的平方-1)
第一题:lim的x趋近于无穷大(x-1)/(x+1)的x次方
第二题:lim的x趋近于1 1/(x-1)减去2/(x的平方-1)
![极限问题(急)第一题:lim的x趋近于无穷大(x-1)/(x+1)的x次方第二题:lim的x趋近于1 1/(x-1)减去](/uploads/image/z/6201004-4-4.jpg?t=%E6%9E%81%E9%99%90%E9%97%AE%E9%A2%98%EF%BC%88%E6%80%A5%EF%BC%89%E7%AC%AC%E4%B8%80%E9%A2%98%EF%BC%9Alim%E7%9A%84x%E8%B6%8B%E8%BF%91%E4%BA%8E%E6%97%A0%E7%A9%B7%E5%A4%A7%EF%BC%88x-1%EF%BC%89%2F%EF%BC%88x%2B1%EF%BC%89%E7%9A%84x%E6%AC%A1%E6%96%B9%E7%AC%AC%E4%BA%8C%E9%A2%98%EF%BC%9Alim%E7%9A%84x%E8%B6%8B%E8%BF%91%E4%BA%8E1+1%2F%EF%BC%88x-1%EF%BC%89%E5%87%8F%E5%8E%BB)
(1)原式等于
lim[1-2/(x+1)]^{[-(x+1)/2]*[-2x/(x+1)]}
=lim{[1-2/(x+1)]^{[-(x+1)/2]}^[-2x/(x+1)]
=e^lim[-2x/(x+1)]
=e^{-2lim[x/(x+1)]}
=(1/e^2)^lim[1-1/(x+1)]
=1/e^2
(2)原式等于
lim[1/(x-1)-2/(x^2-1)]
=lim[(x+1)/(x^2-1)-2/(x^2-1)]
=lim{(x-1)/[(x+1)(x-1)]}
=lim1/(x+1)
=1/2
lim[1-2/(x+1)]^{[-(x+1)/2]*[-2x/(x+1)]}
=lim{[1-2/(x+1)]^{[-(x+1)/2]}^[-2x/(x+1)]
=e^lim[-2x/(x+1)]
=e^{-2lim[x/(x+1)]}
=(1/e^2)^lim[1-1/(x+1)]
=1/e^2
(2)原式等于
lim[1/(x-1)-2/(x^2-1)]
=lim[(x+1)/(x^2-1)-2/(x^2-1)]
=lim{(x-1)/[(x+1)(x-1)]}
=lim1/(x+1)
=1/2
极限问题(急)第一题:lim的x趋近于无穷大(x-1)/(x+1)的x次方第二题:lim的x趋近于1 1/(x-1)减去
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