阿摩線上測驗登入

首頁 > 研究所、轉學考(插大)-微積分 > 105年 - 105 國立臺灣大學轉學生招生考試試題:微積分(B)#110861 >

題組內容

Correctly number each of your answers to indicate which question is answered.

(M) Evaluate dydx. Answer: (14) .

其他申論題

(I) Let u = u(r, y) be a function of t, y. Express in terms of polar coordinates r,θ together with Answer: __(10)__

(J) Find the directional derivative of f(x, y, 2) =xy z2 at the point (e,e, 1) in the direction u = Answer: __(11)__.

(K) Find the critical points of f(x, y) = x2 + y4 + 3xy2 - 5x which are saddle points. Answer:__(12)__.

(L) Find the minimum of x2+ y2 + z2 for (x,y, 2) on the intersection curve of the two surfaces y + 2z = 1 and 3x2 + y2 -z2 = 1. Answer:__ (13)__.

(N) Let R be the region in the first quadrant of the xy-plane bounded by xy = 1, xy = 2, y = 2 and y = 2x. Evaluatedxdy. Answer:____ (15)____.

(O) Evaluate dxdydz, where Ω is given by Ω = {(x,y, 2) : 1≤x2+y2+z2≤2}.Ansuer:__(16)__.

(P) Evaluatedrdydz, whereΩ is the cylinder defined by Ω ={(x,y,z):x2 +y2≤1 and 0 ≤z≤1}. Answer: __(17)__.

(Q) Let S be the surface described by z = x2+ with 4x2+ y2 ≤ 1 oriented with normals with positive k-components. Let F(x,y,z) = xi - yj + k. Evaluate F.dS. Answer:__ (18)__ Also, evaluated.S. Answer: __(19)__.

(R) Let C be the counterclockwise oriented boundary of the region in the xy- plane enclosed byx2 + y2 - 20 = 0 andx2 + y2 - 2y = 0. Evaluate the line integral . Answer:__ (20)__.

(1) 極限=__(1)__。

阿摩線上測驗

提供最完整的考試資料庫，包含歷年試題、詳解、申論題等學習資源，
幫助學生有效準備各類考試。

© 2008-2026 Yamol Tech Ltd. All Rights Reserved.
阿摩線上測驗--最強大的互動線上測驗版權所有

如有任何問題或建議，歡迎聯繫我們