阿摩線上測驗
登入
首頁
>
研究所、轉學考(插大)-微積分
>
100年 - 100 國立暨南國際大學轉學生入學考試試題_資工系二:微積分#124207
>
題組內容
1. (15%)
(c) (5%) Let g(x,y)=x²+ y², prove that ∇g(x, y) = (2x,2y) by the
definition g(x+h) - g(x)= ∇g(x) ⋅ h + o(h).
其他申論題
9. 在y=x2上求距離(0,2)最近的點。
#527955
10. 求
#527956
(a) (5%) Let f(x)=x², prove that f'(x)=2x by the definitionf'(x)=.
#527957
(b) (5%) Let g be a function of several variables which is defined in some neighborhood of 0. We will say that g(h) is o(h) iff = 0.Prove that g(h) = ||h|| is o(h).
#527958
2. (15%) Suppose that the temperature at each point of a metal plane is givenby the function T(x,y)=1+x²-y². Find the path followed by a heat-seekingparticle that originates at (-2, 1).
#527960
3. (10%) Find the directional derivative of the function g(x,y)=x²+y² at thepoint (1, 2) in the direction of the vector 2i-3j.
#527961
4. (10%) Use polar coordinates to calculate the volume of a sphere of radius R.
#527962
5. (10%) Find the interval of convergence of Σ(x+2)k.
#527963
6. (10%) Sketch the graph of the function f(x) = - 5x.
#527964
7. (10%) Evaluate: ∫.
#527965