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96年 - 96 淡江大學 轉學考 應用數學#55961
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1 Show that the area A enclosed by a simply connected curve C : x
2/3
+ y
2/3
= 4 in the x-y plane is 24π. (15 points)
其他申論題
10. The area between two curves y = 2x2 + 3x — 2 and y = x + 2 from x = -1 to x= 2 is= ____
#212130
【已刪除】1. Determine the improper integral dx is convergent or divergent.
#212131
2. A motorcycle shop estimates that it will soil 750 motorbikes in a year. Eacli biko cost $300, plus a fixed charge of $400 per order. If it costs $240 to store a motorbike for a year, what is the order size and how many orders will be needed in a year to minimize inventory costs?
#212132
3. Find the volume under the surface f(x,y)= xe-y over the region which is bounded by curves y = 1-x2, x=0 and y = 0.
#212133
2. A matrix is both Hermitian and Unitary. Show that its eigenvalues are ±1, (15 points)
#212135
【已刪除】3. Find (he Laplace transformation of the square wave with period of a defined by(15 points)
#212136
【已刪除】4. Suppose that/(jc) = jc',/2is a self-reciprocal under Fourier cosine transform, apply the given result and evaluate the Fresnel integral (15 points)
#212137
【已刪除】5’ Given =π ln 2, show that (15 points)
#212138
6, Given/(jc) = (x + 1)2,-1≤x≤1) expand f(x) in terms of Legendre polynomials. (10 points)
#212139
【已刪除】7. (a) Write down ftinction form of Legendre polynomials (5 points)
#212140
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