89年 - 89 國立政治大學轉學生招生考試_應用數學系：微積分(二)#122908

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2. Find the interval of convergence for the power series. (20%)

3. Let Show that the partial derivatives for fx and fy exist at the origin, but f is not differentiable there. (15%)

4. Find the point on the intersection of the plane and the paraboloid that is closest to the origin. (15%)

5. Evaluate sin(x+2y) cos(x-2y) dA over the region R = {(x, y) | x ≥ 0, y ≥ 0, x + 2y ≤ 2π}. (15%)

6. In an inverse square force field, where c is a constant and , find the work done in moving a particle along the line from (1, 1, 1) to (3, 3, 3). (15%)