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3. Find the maximum value of dy, where C is any circle in the xy-plane, oriented counterclockwise.

其他申論題

(a) (6 分) In what direction from (-1,2) does the temperature increase most rapidly? What is this rate of increase?

(b) (6 分) Find the path of the particle as it continuously moves in the direction of maximum temperature increase.

1. How many critical points does the function f(x) =|x2 - 1|have? Answer :________

2.If = 1, then a-b=? Answer :_________

3. Suppose f" is continuous on [0,1], f(1) = 2, f'(1) = 2 and the average value of f on [0, 1] is 2. Evaluate dx. Answer :__________

4. Find g', where g(x) is the inverse of f(x) = . Answer :___________

5. Find the directional derivative of f(z,y) = at P0(1,1) in the direction of v= .Answer :__________

6. Evaluate dydx. Answer:_______

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