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理学
问答题
问答题计算曲线积分，其中L为从点A(1，0)沿上半圆周x2+y2=1到点B(-1，0)的一段弧．
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问答题设向量组
α
1
=(1，1，1，3)
T
，α
2
=(-1，-3，5，1)
T
，α
3
=(3，2，-1，p+2)
T
，α
4
=(-2，-6，10，p)
T
．
(Ⅰ)p为何值时，该向量组线性无关?并在此时将向量α=(4，1，6，10)
T
用α
1
，α
2
，α
3
，α
4
线性表示；
(Ⅱ)p为何值时，该向量组线性相关?并在此时求出它的秩和一个极大线性无关组．
问答题设f(x)在x=0邻域有连续的导数，又f(0)=0，求证：F(x)在x=0有连续导数．
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问答题将展开成x的幂级数．
问答题计算，[x]表示不超过x的最大整数．
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问答题证明方程2x=x2+1有且仅有三个实根．
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问答题{{B}}Directions:{{/B}} Read the following passage carefully and then translate each
underlined part into Chinese.71.{{U}}The international software
market represents a significant business opportunity for U.S. microcomputer
software companies, but illegal copying of programs is limiting the growth of
sales abroad. If not dealt with quickly, international piracy of software could
become one of the most serious trade problems faced by the United
States{{/U}}. 72. {{U}}Software piracy is already the biggest
barrier to U.S. software companies entering foreign markets. One reason is that
software is extremely easy and inexpensive to duplicate compared to the cost of
developing and marketing the software. The actual cost of duplicating a software
program, which may have a retail value of $ 400 or more, can be as little as a
dollar or two—the main component being the cost of the diskette{{/U}}. 73. {{U}}The
cost of counterfeiting software is substantially less than the cost of
duplicating watches, books, or blue jeans. Given that the difference between the
true value of the original and the cost of the counterfeit is so great for
software, international piracy has become big business. Unfortunately, many
foreign governments view software piracy as an industry in and of itself and
look tile other way{{/U}}. U.S. firms stand to lose million of
dollars in new business, and diminished U.S. sales nut only harm individual
firms but also adversely affect the entire U.S. economy.
问答题
问答题设A为3阶矩阵，α1，α2，α3是线性无关的3维列向量，且Aα1=α2-α3，Aα2=3α1-2α2+α3，Aα3=3α1+2α2-3α3．