若点(x0,f(x0))(x_{0},f(x_{0}))(x0,f(x0))是曲线y=f(x)y = f(x)y=f(x)的拐点,且f′′(x0)f^{\prime\prime}(x_{0})f′′(x0)存在,则一定有( ).
(A)f′′(x0)=0f^{\prime\prime}(x_{0}) = 0f′′(x0)=0
(B)f′(x0)f^{\prime}(x_{0})f′(x0)
(C)f′′(x0)>0f^{\prime\prime}(x_{0})>0f′′(x0)>0
(D)f′′(x0)<0f^{\prime\prime}(x_{0})<0f′′(x0)<0
计算定积分∫0211+2xdx\int_{0}^{2}\dfrac{1}{1 + \sqrt{2x}}dx∫021+2x1dx.
设直线y=2−xy = 2 - xy=2−x,y=0y = 0y=0与曲线y=x2(x≥0)y = x^{2}(x\geq0)y=x2(x≥0)所围成的平面图形为DDD.
(1)求DDD的面积SSS;
(2)求DDD绕xxx轴旋转一周所得旋转体的体积VVV.
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