95年 - 95 淡江大學轉學考_理工組二年級：微積分#56156

科目：研究所、轉學考(插大)-微積分 | 年份：95年 | 選擇題數：0 | 申論題數：13

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (13)

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(3) The position (位置)of a particle is given by ihe equation s = f(t) 1/(1+t), where t is measured in seconds (秒)and s in meters (米).The velocity (速度)after 2 seconds is ?

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(6) Let f (x,y)=xe^y.frnd the maximun rate of change of f at the point(2,0).

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【已刪除】(8) Find the interval of convergence (收斂區間)of the power series

(9) Show that the parabola y = -x² and ihe line x-4y- 18 = 0 intersect al right angle al one of their points of intersection (於二個交點之一以直角相交）.

(10) A ladder (梯）10 feet long rests against a vertical wall (斜靠於一垂直牆面).of the bottom (底）of the ladder slides away (滑開）from the wall at a rate of 1 fl/sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6ft from the wall?

(11) Find the volume of the solid obtained by rotating (旋轉)the region (區域)bounded by y=x- x² and - 0 about Ihe line x = 2

【已刪除】(12) Determine wheLlter

converges absolutely, converges condhionally, or diverges (要清楚寫出判斷之依據)

(13) Tlie plane x+y+z = 1 cuts ( 切過）the cylinder (圓柱）x² + y² = 1 in an ellipse (橢圓）.Use Lagrange multipliers lo find the points on the ellipse that lie closest to (最近)and farthest from (最遠)the origin (原點）.