阿摩線上測驗
登入
首頁
>
研究所、轉學考(插大)-微積分
>
110年 - 110 國立臺灣大學_碩士班招生考試_大氣科學研究所乙組:微積分(A)#102182
>
題組內容
3. Investigate the integral
(b) (4 pts) Write
as the sum of a power series
其他申論題
(b) (6 pts) Sketch the graph of f(x), indicating intervals of increasing/ decreasing, and concavity.
#429799
(a) (10 pts) How should he choose the point C to minimize the total time ?
#429800
(b) (6 pts) If he runs m tines as fast as he swims, how will his best strategy be modified as m varies (m ≥ 1) ?
#429801
(a) (7 pts) Show that the improper integral dx converges. Show that
#429802
(c) (6 pts) Write Ina dx as the sum of a series. Thus, wecan use its partial sums to estim mate the integral.
#429804
4. (10 pts) Find the twice differentiable function f(x) such that
#429805
(a) (5 ps), the gradient of f.
#429806
(b) for (x, y)≠ (0,0) and f(0,0) = 0. Compute the directional derivative of f along u = (cosθ, sin θ) at (0,0).
#429807
6. (10 pts) Find the critical points of f(x, y), where z = f(x, y) satisfies the equation yz+x Iny = z2. Are these critical points local maxinum, local minimum, or saddle points?
#429808
(a) (7 pts)
#429809
as the sum of a power series
阿摩線上測驗
登入
阿摩線上測驗
登入
as the sum of a power series