分子有理化
根號(hào)[(x-1)(x-2)]-x= (根號(hào)[(x-1)(x-2)]-x)(根號(hào)[(x-1)(x-2)]+x)
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根號(hào)[(x-1)(x-2)]+x
=[(x-1)(x-2)-x^2]/[根號(hào)[(x-1)(x-2)]+x]=(-3x+2)/[根號(hào)[(x-1)(x-2)]+x]
上下同除x
=(-3+2/x)/[根號(hào)[(1-1/x)(1-2/x)]+1]
當(dāng)x趨向無(wú)窮,分子->-3+0=-3
分母->1+1=2
所以極限為-3/2