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7. Let Rbe the solid inside x²+ y²+ z²= 1, outside z = and above the xy-plane. Find the volume of R. Answer :___________

其他申論題

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:_______

8. Evaluate the line integral dy, where C : boundary of the region lying between the graphs of the ellipse = 1 and the circle x2 + y2 = 1. Answer:_______

1Find any extrema of the function subject to the constraint x2 + y2≤ 1.

2. For the function show that fx(0,0) and fy(0,0) both exist, but that f is not differentiable at (0, 0).

3. Determine whether the seriesconverges absolutely or conditionally, or di-verges.

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