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题目：（满分14分）已知曲线Cn：x^2-2nx＋y^2=0（n=1,2,…）.从点P（-1,0）向曲线Cn引斜率为kn（kn〉0）的切线lm切点为Pn（xn,yn）.
（1）求数列{xn}与{yn}的通项公式;（2）证明：x1·x3·x5…x2n-1〈√1-xn/1＋xn〈√2 sinxn/yn. 相似文献
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文 [1]给出了条件 x+ y=1下 1xn+ λyn的最小值定理 ,并利用 (a2 + b2 ) (c2 + d2 )≥ (ac+ bd) 2 (a,b,c,d∈ (0 ,+∞ )和待定系数法证明之 .定理 已知 x,y,λ∈ (0 ,+∞ )且 x+ y=1,则当且仅当 y∶ x=λ1n+ 1 时 ,1xn+ λyn(n∈N* )取最小值 ,最小值为 (1+ λ1n+ 1 ) n+ 1 .本文给出定理的一个简单证明 .证明 ∵x,y,λ∈ (0 ,+∞ ) ,n∈ N* ,且x+ y=1,∴ 1xn+ λyn=(1xn+ λyn) (x+ y) n =(1xn+λyn) (C0nxn+ C1 nxn-1 y+ C2nxn-2 y2 +… + Crnxn-ryr+… + Cnnyn)=1+ C1 nyx + C2ny2x2 +… + Crnyrxr +… + Cnnynxn+ λC0nxnyn + … 相似文献
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柯西不等式是高中数学中重要的不等式之一,它有如下重要变式：
若xi,yi∈R＋（i=1,2,...n,n∈N^＊,n≥2）,则有x^21/y1＋x^22/y2＋...＋x^2n/yn≥（x1＋x2＋...＋xn）^2/y1＋y2＋...＋yn,当且仅当x1/y1=x^2/y2=...=xn/yn时等号成立． 相似文献
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李庆元 《河北工程技术职业学院学报》2003,5(3):37-38
本着眼于渐进准非扩张算子的具有误差的Ishikawa迭代序列：xn 1=(1-αn)xn αnT'yn un yn=(1-βn)xn βnT'xn vn(n∈N） （αnβn∈[0,1]),的收敛性的研究，获得了其收敛于不动点的一个充分必要条件。 相似文献
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关于两类递推数列的极限 总被引：1，自引：0，他引：1
根据不动点的定义和存在性定理 ,证明了两类递推数列 {xn 1=f(xn) }与 { yn 1=[f( yn) yn] / 2 }的极限存在 ,并且给出了计算它们的极限的方法。 相似文献
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给出了广义的Logisitc映射和θ=2时,系统log(xn 1)-log(xn)=r(1-xn2),0相似文献
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设{x n}是满足递推关系x0=1,x1=a>1,xn+2=2a x n+1-xn的数列.本文给出了:a=5,9,169以及9 801时所有可使xn是平方数的正整数n. 相似文献
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根据费马大定理，运用基础数论的方法，证明了不定方程X^nY^nZ^n=（X^n＋Y^n）^n＋2，（n≥3）没有正整数解。 相似文献
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吴强 《湖南第一师范学报》2007,7(4):157-158
Fibonacci矩阵是一种特殊的二阶矩陈,广义Fibonacci矩阵是m(m>2)阶的Fibonacci矩阵,在广义Fibonacci矩阵集合中,方程xn yn=zn,n∈N,没有解(n,x,y,z)。 相似文献
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Fibonacci矩阵是一种特殊的二阶矩陈,广义Fibonacci矩阵是m(m>2)阶的Fibonacci矩阵,在广义Fibonacci矩阵集合中方程xn yn=zn,n∈N,没有解(n,x,y,z). 相似文献
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乐茂华 《湖州师范学院学报》2007,29(1):15-16
设n是正整数,φ(n)是Euler函数.证明了方程xn yn=zφ(n)当且仅当n≤3时有正整数解(x,y,z)适合gcd(x,y)=1. 相似文献
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《海外英语》2007,(4):36
There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love. 相似文献
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Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject. 相似文献
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Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities. 相似文献