所屬科目:研究所、轉學考(插大)-微積分
1.=________.
2.=__________.
3.=_________.
4.=___________.
5. =_________.
6.x2+y2+xu+yu+2uU=6, xy-uU+u-0=0.、At (x,y,u,U)=(1,1,1,1),=_______,=_________.
7. The function In increases the fastest in the direction of_______ at (1,0).
8. The function dt where x has maximum at _________and the minimum value is __________.
10 points for each problem. Solve the problems with the process shown, not just give the answers.
9. Find the 'Taylor series expansion for the function at x = 0.
10. A storage silo consists of a right circular cylinder with a hemispherical top. If the silo is to have a fixed volume, find the dimensions of the silo of this type of the minimal surface area. (A sphere with radius a has surface area 4πa2 and volume .)