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研究所、轉學考(插大)-微積分
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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
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4. (10 pts) Find the twice differentiable function f(x) such that
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(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) ?
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(a) (7 pts) Show that the improper integral dx converges. Show that
#429802
(b) (4 pts) Write as the sum of a power series
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(c) (6 pts) Write Ina dx as the sum of a series. Thus, wecan use its partial sums to estim mate the integral.
#429804
(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)
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(b) (8 pts)
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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
#429811
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