lim(x趋向+∞)[根号(x+1)-根号x]怎么求
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lim(x趋向+∞)[根号(x+1)-根号x]怎么求
lim(x趋向+∞)[根号(x+1)-根号x]怎么求
lim(x趋向+∞)[根号(x+1)-根号x]怎么求
limx->+∞ [√(x+1)-√x]
=limx->+∞ [√(x+1)-√x][√(x+1)+√x]/[√(x+1)+√x]
=limx->+∞(x+1-x)/[√(x+1)+√x]
=limx->+∞ 1/[√(x+1)+√x]
=limx->+∞ 1/√x[√(1+1/x) +1]
=limx->+∞ 1/√x *limx->+∞ 1/[√(1+1/x) +1]
=0*1/[(1+0)+1]
=0
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