所屬科目：研究所、轉學考(插大)-微積分
(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) ?
(a) (7 pts) Show that the improper integral dx converges. Show that
(b) (4 pts) Write as the sum of a power series
(c) (6 pts) Write Ina dx as the sum of a series. Thus, wecan use its partial sums to estim mate the integral.
4. (10 pts) Find the twice differentiable function f(x) such that
(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).
(a) (7 pts)
(b) (8 pts)
8. (10 pts) Let S be the part of the cylinder x2+y2 = 2y that lies in the sphere x2 +y2 +z2 = 4 and inside the first quadrant. Compute
阿摩線上測驗
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阿摩線上測驗
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dx converges. Show that
as the sum of a power series
Ina dx as the sum of a series. Thus, we
, the gradient of f.
for (x, y)≠ (0,0) and f(0,0) = 0. Compute the directional derivative of f along u = (cosθ, sin θ) at (0,0).
