第二和第十题,求极限,求过程
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2、原式
=lim(h→0)[(x^3+3x^2h+3xh^2+h^3)-x^3]/h
=lim(h→0)(3x^2+3xh+h^2)
=3x^2
10、原式
=lim(x→1)[x^(1/3)-1][x^(2/3)+x^(1/3)+1][x^(1/2)+1]/{[x^(1/2)-1][x^(1/2)+1][x^(2/3)+x^(1/3)+1]}
=lim(x→1)[x-1][x^(1/2)+1]/{[x-1][x^(2/3)+x^(1/3)+1]}
=lim(x→1)[x^(1/2)+1]/[x^(2/3)+x^(1/3)+1]
=(1+1)(1+1+1)
=2/3
=lim(h→0)[(x^3+3x^2h+3xh^2+h^3)-x^3]/h
=lim(h→0)(3x^2+3xh+h^2)
=3x^2
10、原式
=lim(x→1)[x^(1/3)-1][x^(2/3)+x^(1/3)+1][x^(1/2)+1]/{[x^(1/2)-1][x^(1/2)+1][x^(2/3)+x^(1/3)+1]}
=lim(x→1)[x-1][x^(1/2)+1]/{[x-1][x^(2/3)+x^(1/3)+1]}
=lim(x→1)[x^(1/2)+1]/[x^(2/3)+x^(1/3)+1]
=(1+1)(1+1+1)
=2/3
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