一道极限题
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((x+1)^(3/2)-x^(3/2))/x^(1/2)
=((x+1)³-x³)/(x^(1/2)((x+1)^(3/2)+x^(3/2)))
=(3x²+3x+1)/(x^(1/2)(x+1)^(3/2)+x^4)
=(3x²+3x+1)/(x^(1/2)(x+1)^(3/2)+x²)
=(3+3/x+1/x²)/(1+((x+1)/x)^(3/2))
=3/(1+1)
=3/2
=((x+1)³-x³)/(x^(1/2)((x+1)^(3/2)+x^(3/2)))
=(3x²+3x+1)/(x^(1/2)(x+1)^(3/2)+x^4)
=(3x²+3x+1)/(x^(1/2)(x+1)^(3/2)+x²)
=(3+3/x+1/x²)/(1+((x+1)/x)^(3/2))
=3/(1+1)
=3/2
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