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98年 - 98 中原大學轉學生招生考試_理工群組二、 化學群組二、 資工二:微積分#124593
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1. Define f(x, y) =
for x, y
. Show that f is not differentiable at (0,0).
其他申論題
7. =_________
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8. If f(x,y) = , for x >0 and y , then =_________
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9. The equation for the tangent plane to the surface x2 + 4y2 + 9z2 = 3 at the point is ________.
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10. The shortest distance between the parabola y = x2 and the point (6, 3) is ________.
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2. Let f(x) =Show that f is differentiable at each x and that f' is not continuous at 0.
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3. Two right circular cylinders of radius 1 have axes that intersect at right angles. Find the volume of the solid common to the two cylinders.
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(a) (5%)
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(b) (5%) does not exist
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(a) (5%) Find
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(b) (5%) Evaluate
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