应JJ要求 愿大家考试顺利 如果万一万一万一考差了 没关系~张秋骏会是你永远的好朋友 祝万福万安~~~ ※ [本文转录自 NTU-Exam 看板] 作者: cawaiik (5/1台大热舞成发在旧体) 看板: NTU-Exam 标题: [试题] 93下 张秀瑜 微乙 期末考题 时间: Fri Aug 19 17:03:34 2005 课程名称︰微积分乙 课程性质︰ 课程教师︰张秀瑜 开课系所︰管院 考试时间︰93下 试题 : 1. Find dz/dz if z is defined implicitly as a function of x and y by the equation sin(xyz) = x + 2y + 3z . 2. Show that f(x,y) = x√y is differentiable at (1,4) and find its linearization there. Then use it to approximate (1.1,3.9) . 3. If z = f(x,y) has continuous second-order partial derivatives and x = r^2 + s^2 and y = 2rs , find (a) dz/dr and (b) d^2z/drds . 4. Consider the curve xsin(x+y) + 2x^2 = 0 in xy-plane. Find a vector which is orthogonal to the curve at (1/2, 3π-1 / 2) 5. (a) Find the volume of the solid under the plane x + 2y - z = 0 and above the region bounded by y = x and y = x^4 1 1 ________ (b) Evaluate ∫ ∫ √x^3 + 1 dxdy by reversing the order of 0 √y integration. 6. Evaluate ∫∫ xdA , where D is the region in the first quadrant D that lies between the circles x^2 + y^2 =4 and x^2 + y^2 = 2x . 7. Evaluate ∫∫∫ (x^2 + y^2 + z^2)dV , where E: 0 ≦ z , E x^2 + y^2 + z^2 ≦ 1 . 8. Evaluate ∫∫ sin(9x^2 + 4y^2)dA , where R is the region in the R first quadrant bounded by the ellipse 9x^2 + 4y^2 = 1 . --

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