1.The temperature T(x,y) at points of the xy-plane is given by T(x,y) = x^2 - 2y^2 . In what direction should an ant at position (2,-1) move if it wishes to cool off as quickly as possible? 它题目要求温度能急速下降，表示温度变化率最大，所以我初步猜测 应该是▽T (因为T的方向导数(温度沿某弧长方向的变化率) dT/ds = ▽T‧T = │▽T│ ≦cosθ) 但它是怎麽判断该变化率是温度急遽升高还是下降???? 题目要求快速下降，但我不知道结果出来的变化率会导致上升还是下降? 2.Prove d g(x) ---- ∫ f(u)du = f(g(x))g'(x) . dx a 此题如果用Leibniz，算不算正当证法? 3.Compute ∫∫ lnx dA , where D is the finite region in the first quadrant D bounded by the line 2x+2y = 5 , and the hyperbola xy = 1. 这一题没加lnx很简单，加上去以後我就不知道该怎麽积了@@" x^2 y^2 z^2 4.Find the volume of the region inside the ellipsoid --- + --- + --- =1 a^2 b^2 c^2 and above the plane z = b-y. 这题我主要卡在积分域不知道该怎求~ --

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