作者jech801127 (cosmos)
看板NTU-Exam
标题[试题] 99下 张秀瑜 微积分乙下 第二次期中考
时间Wed Jun 22 00:04:59 2011
课程名称︰微乙
课程性质︰必修
课程教师︰张秀瑜
开课学院：理学院
开课系所︰经济/管院/地理
考试日期（年月日）︰2011/5/24
考试时限（分钟）：110分钟
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（如未明确表示，则不予发放）
试题 :
1.(24%)Find the following partial derivatives. Assume all functions
are differentiable.
x ∂f
(1)f(x,y)=∫cos(t^2)dt. find ___
y ∂x
∂u
(2)u(x,t)=f(x+at)+g(x-at). find ___
∂t
∂z ∂ ∂z
(3)z=f(x,y), x=rcosθ, y=sinθ, find_____ and ___(___ )
∂θ ∂r ∂x
2.(10%) If f(x,y)=(y+x^5)^1/5, find fx(0,0)
3.(15%) Let f(x,y)=tan^-1(x+2y)
(a)Explain why f is differentiable?
(b)Find the linearization L(x,y) of f at the point (1,0)
→
(c)Find Duf(1,0), where u=(√2/2, √2/2)
4.(10%) Use differentials to estimate the amount of tin in a closed tin can
with diameter 8cm and height 12cm if the tin is 0.05cm thick.
5.(12%) Find equations of
(a)the tangent line and
(b)the normal line to the surface x^2+2y^2-3z^2=3 at the point(2,-1,1)
6.(16%) Find the extreme values of f(x,y)=e^-xy on the region inside x^2+4y^2=1
7.(16%) Find the local maximum and minimum values and saddle points of
f(x,y)=2x^3+xy^2+5x^2+y^2
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