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3. Convert the integral dzdydx to an equivalent integral in cylindrical coordinates.
Answer :__________(Do not evaluate the integral).

其他申論題

9. Find the absolute maximum value and absolute minimum value of f(x,y) =x4+y4 -4xy + 1 on the disk x2+y2≤1.

10. Solve the differential equation xy' = y + x2 sin x with y(π) = 2π.

1. If f'(0) =-1, find.Answer : ________

2. Find dt. Answer:_________

4. Evaluate the integral Answer : ____________

5. Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y- z = 0. Answer :__________

6. The derivative of f(x, y) at P0(1, 2) in the direction of i + j is and in the direction -2j is -3. What is the derivative of f in the direction of -i -2j?Answer :__________

7.the area of cap cut from the sphere x2 + y2 + z2 == 2 by the cone z =.Answer :__________

8. Evaluate the line integral f where C consists of line segments joining successively the points (1,0), (I, 1), (-1, 1) and (-1,0). Answer : __________

(a) Show that f'(0)=0.(6分)

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