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-阿摩線上測驗
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
1. Suppose that f(x) satisfes the equation f(x +y)= f(x)+ f(y) + xy - x2y - xy2 for all
(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) ?
3. Investigate the integral
(a) (7 pts) Show that the improper integral dx converges. Show that
(c) (6 pts) Write
Ina dx as the sum of a series. Thus, we
can use its partial sums to estim mate the integral.
(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).