1、有理化
lim[x→4] [√(2x+1)-3][√(2x+1)+3](√x+2) / (√x-2)(√x+2)[√(2x+1)+3]
=lim[x→4] (2x+1-9)(√x+2) / (x-4)[√(2x+1)+3]
=lim[x→4] 2(x-4)(√x+2) / (x-4)[√(2x+1)+3]
=lim[x→4] 2(√x+2) / [√(2x+1)+3]
=8/6
=4/3
2、lim[n→∞] (1+2+...+n)/(n+2) - n/2
=lim[n→∞] (1/2)n(n+1)/(n+2) - n/2
=lim[n→∞] (1/2)[n(n+1)/(n+2) - (n²+2n)/(n+2)]
=lim[n→∞] (1/2)[-n/(n+2)]
=-1/2
3、题目是否应为x→+∞?分子有理化
lim[x→+∞] [√(x+5) - √x]
=lim[x→+∞] [√(x+5) - √x][√(x+5) + √x]/[√(x+5) + √x]
=lim[x→+∞] 5/[√(x+5) + √x]
=0
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