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研究所、轉學考(插大)-微積分
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92年 - 92 國立暨南大學轉學生招生考試試題_微積分_(土木系)#125371
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題組內容
3. Evaluate the Integrations: (4 pts for each question, total 20 pts)
(e)
其他申論題
(a)
#533258
(b)
#533259
(c) ∫ cosx ln(sinx) dx
#533260
(d)
#533261
(a) f(x) = sinx at x = 0
#533263
(b) f(x,y) = sinxcosy at (0, π)
#533264
5. Find the velocity and acceleration vectors for the position vector r(t) = (4cos2t, 4sin2t, 4t) at t = π/4.
#533265
6. Prove that the Taylor expansion of sinx at x is sinx = and use it to approximate dx with first 3 terms (i.e., n=3).
#533266
7. (a) Use Jacobian between Cartesian coordinates and polar coordinates to derive the evaluation formula for polar coordinates: (x, y) dxdy = (rcosθ, rsinθ) rdrdθ
#533267
(b) Evaluate 2xdydx by converting to polar coordinates using the formula of (a).
#533268
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