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94年 - 94 國立暨南大學轉學生招生考試試題_微積分_(土木系)#125169
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3. Find the velocity and acceleration vectors for the position vector
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(b)
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(c)
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(d)
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(e)
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4. Symbolically find δ in terms of ε for
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5. Find the Maclaurin series of and its interval of convergence. Also, use it to determine the value of
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6. Find a vector function that represents the curve of intersection of the cylinder x² + y² = 4 and the plane y+z=2 with parameter t. Also, find the arc length of the intersection curve for 0≤t≤π.
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(a) Find the domain of by the Ratio Test.
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(b) Show that satisfies the differential equation: , where and are the second and first derivative of , respectively.
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(c) Evaluate the first 3 terms of without calculating the number.
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