求函数f(x)=x3−27xf(x)=x^{3}-27xf(x)=x3−27x的单调区间和极值.
设由方程exy−xy2=e2e^{xy}-xy^{2}=e^{2}exy−xy2=e2确定的函数为y=y(x)y = y(x)y=y(x)，求dydx∣x=0\left.\dfrac{dy}{dx}\right|_{x = 0}dxdyx=0.
若limx→∞(x−bx)x=e3\lim\limits_{x \to \infty}(\dfrac{x - b}{x})^x = e^3x→∞lim(xx−b)x=e3，求bbb的值.
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