推 hips:誰有線代第二次考題的現在快po一下,我把我所有p幣都送你.. 05/02 01:05
課程名稱︰微積分乙
課程性質︰共同必修
課程教師︰陳其誠
開課學院：管院
開課系所︰管院各系
考試日期（年月日）︰2007/05/01
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
試題 :
Write down your answers on the answer sheet. You should include all
the necessary calculations and reasoning.
(1)For the following functions find the partial derivative fx
(a)f(x,y)=e^-(x^2+y^2)
(b)f(x,y,z)=sin(y+z)
(c)f(x,y,z)=2x√y - 1/(x^2)y
(2)Find fxy,if f(x,y)=xy/(x^2 + y^2)
(3)Find the following limits:
(a) lim sinπ(x+y)/6 / cosπ(-x+y)/6
(x,y)→(1,2)
(b) lim xy/(x^2 + y^2)
(x,y)→(0,0)
(c) lim xy^2/(x^2 + y^2)
(x,y)→(0,0)
(4)Suppose f(x,y) is a polynomial in x,y and the gradient ▽f(3,4)=(5,12).
If v=(3/5,4/5),then the directional derivative Dvf(3,4)=?
Find the unit vector u=(u1,u2) such that the directional derivative
Duf(3,4)=13.
(5)Suppose f(x,y)=√(9x^2 + 4y^2) and z = A + B(x-1) + C(y-2) is the equation
of the tangent plan to the surface z=f(x,y) at the point(1,2,5).
Find the values of A,B,C.
(6)Two chemicals X and Y can cause some change of temperature in an organic
system. It is known that the temperature will increase F(x,y)
centigrade (。C),if a total amount of x gram of X together with y gram of Y
is injected into the system. And F is a differentiable function of x,y.
It is also known that if one, with a constant speed 1g/sec, inject X (resp.
Y) into the system then the temperature will increase with the speed
5(。C/sec) (resp. 1(。C/sec)). In what speed will the temperature increase,
if we injest both with the constant speed 3g/sec for X and 4g/sec for Y?
Why?
(7)Find the equation of the tangent line to the curve x^2007 + 501xy - 2y^8 +
9=500 at the point (1,2)
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