阿摩線上測驗
登入
首頁
>
研究所、轉學考(插大)-微積分
>
107年 - 107 台灣聯合大學系統(清華、交通、陽明、中央四校聯招)學士班轉學生考試_A3、A4、A7:微積分#112635
>
題組內容
1. A heat-seeking particle is located at the point (-1,2) on a metal plate whose temperature at (x, y) is T(u,u) = 64-2x
2
y
2
.
(a) (6 分) In what direction from (-1,2) does the temperature increase most rapidly? What is this rate of increase?
其他申論題
5. Find the surface area of the portion of the plane z = 4 - 2x - 2y that lies above the circlex2+y2≤1 in the first quadrant. Answer :__________
#482784
6. Find an equation of the tangent plane to the paraboloid r(u,u) = ui + uj + (u2 +u2)k at the point (1,2,5), Answer :____________
#482785
7. Evaluate the integraldxdy. Answer:___________
#482786
8. Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R : region bounded by the parallelogram with vertices (0,0),(1,1), (5,0) and (4, -1): Answer:____________
#482787
(b) (6 分) Find the path of the particle as it continuously moves in the direction of maximum temperature increase.
#482789
a. (6分)
#482790
b. (6分)
#482791
3. Find the maximum value of dy, where C is any circle in the xy-plane, oriented counterclockwise.
#482792
1. How many critical points does the function f(x) =|x2 - 1|have? Answer :________
#482793
2.If = 1, then a-b=? Answer :_________
#482794