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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_(資工系)#124709
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題組內容
2. Let f(x,y) = 1 + x² + y².
(a) (6%) Find the points (x,y), if any, at which ∇f(x,y) = 0.
其他申論題
9. 求出 f(x, y, z) = sin xy + ln xz + z 沿著 r(t) = et i + t２j + k 對 t 之變化率。
#530528
10. 求ex² dxdy , 先畫出積分區域Ω,然後改變積分順序。
#530529
(a) (7%) Calculate g(h).
#530530
(b) (13%) Show that, of all lines that pass through (x, f(x)), the tangent line is the line that best approximates the graph of f near the point (x, f(x)) byshowing thatg(h) = o(h) iff m = f'(x).
#530531
(b) (6%) Sketch the graph of the surface z = f(x,y).
#530533
(c) (8%) Determine the path of steepest descent along the surface z = f(x,y)from the point (1, 1, 3).
#530534
(a) (12%) Prove that ln(ab) = ln(a) + ln(b) for a, b ＞ 0.
#530535
(b) (8%) By (a), to prove ln(1/b) = -ln(b) and ln(a/b) = ln(a) - ln(b).
#530536
(a) (8%) Find the area of the region R bounded by the graph of f and thex-axis.
#530537
(b) (12%) Find the volume of the solid generated by revolving R around thex-axis.
#530538
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