94年 - 94 國立成功大學轉學生招生考試試題_微積分_(全校)#115148

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6.Find the third Taylor polynomial of f(x) = sin(sinx) at 0 (i.e., the Taylor polynomial of f(x) up to the term x³).

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8.The plane x + y + 2z = 2 intersects the paraboloid z =x² + y² in an ellipse.Find the point on the ellipse that is farthest from the origin.

9.Find the volume of the solid bounded by the paraboloid z = 1 - x² - y² and the plane z = 0.

10.Evaluate the line integral ∫c Fㆍdr, where F(x, y, z) = -y²i + xj + x²k and C is the curve of intersection of the plane z = 2 and the cylinder x² + y²= 1. (Orient C to be counterciockwise when viewed from above.)

94年 - 94 國立成功大學轉學生招生考試試題_微積分_(全校)#115148

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