1.求下列函数的导数: (1)y=(2x2-x+1)2;

8用两种顺序计算∫ddy,D:y=x与y=x2所围区域

1.设y(x)在[0,+∞)上连续且单调,limy(x)=0,证明

1.计算下列积分: (1)x-x2dx; (2)dx

Problem Set 1 Prof. Gene Chang Due on Dec.5 5th in the class,orta' 's office(经院220室) Late turn-in may result in a penalty in the grade 1. The consumption set is={x X E}. Suppose the utility function representing the preference

1.利用Green公式计算下列积分: (1)f(x+y)2dx-(x2+y2)dy,其中L是以A(11),B(32)C(25)为顶点的三角形的边界,逆时针方向;

1.求下列第二类曲线积分: (1)(x2+y2)dx+(x2-y2)dy,其中L是以

仍然是已知 x1 … xm ; y1 … ym, 求一个简单易算的近似函数 f(x) 来拟合这些数据

原理：若 f(x) C[a, b]，且 f (a) · f (b) <0，则f(x) 在 (a, b) 上必有一根

Problem Set 3 Prof. Gene Chang (For Ph. D students, due on Dec. 28th in the class, or TA's office. For M.A. students, due on Dec. 26th, in the class or TA's office. Late turn-in may result in a penalty in the grade) 1. Kland is a Robinson Crusoe type economy. Robinson, as the consumer and the owner of the firm, has the utility function U(x,) =aIn x+ BInI, where is leisure. Robinson's endowment