《最终幻想13：雷霆归来》凶斩极限伤害图解
《最终幻想13：雷霆归来》凶斩极限伤害图解
《最终幻想13：雷霆归来》凶斩最高伤害是多少呢?今天小编就为大家带来玩家“白衣死
神MOMO”整理分享的《最终幻想13：雷霆归来》凶斩极限伤害图解，下面赶快跟我一起来看看吧。【本文转自贴吧】
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极点极限定理的简单应用
一道高考解析几何题的背景溯源 ──极点、极线与圆锥曲线的位置关系 湖北省阳新县高级中学邹生书 题目已知椭圆的两个焦点，点满足，则 的取值范围是，直线与椭圆的公共点的个数是. 这是2010年高考湖北卷文科第15题，本题是一道涉及到点、直线与圆锥曲线的位置关系的判定的考题．从高等几何的观点知，这里的点和直线就是椭圆 的一对极点与极线，本题第二问实际上是：已知椭圆的极点在椭圆内，判断极线与椭圆的位置关系．据笔者之前发表的文章中圆锥曲线极点和极线的几何性质可得如下结论： 定理已知点和直线是圆锥曲线的一对极点与极线．（1）若极点在曲线上，则极线与曲线的相切于点；（2）若极点在曲线内，则极线与曲线的相离；（2）若极点在曲线外，则极线与曲线的相交． 由该定理不难知道，考题中的直线与椭圆相离，故公共点个数为0．若运 用几何画板进行实验操作动态演示，不仅可以验证确认该结论，而且还可获得直观感知从而加深印象强化理解．本文将借用判别式法给出该定理的另一种证明． 为了表达方便我们给出圆锥曲线内部和外部的定义．圆、椭圆是封闭图形其内部和外部不言而喻，抛物线、双曲线不是封闭的是开的，我们参考一些杂志专著，对双曲线和抛物线的内部和外部给出如下定义：焦点所在的平面区域称为该曲线的内部，不含焦点的平面区域称为曲线的外部，曲线上的点既不在内部也不在外部．关于点与圆锥曲线位置关系我们有如下结论（这里证明从略）． 引理1已知点和抛物线．则（1）点在上 ；（2）点在内；（3）点在外．
引理2 已知点和椭圆（或圆）．则（1）点在 上；（2）点在内；（3）点在外．引理3已知点和双曲线．则（1）点在上 ；（2）点在内；（3）点在外．圆锥曲线把平面上的点分成三个部分：曲线上的点、曲线内的点和曲线外的点，每一部分的点的坐标对于曲线方程的左右两边的值具有相同的大小关系，真是“物以类集，人以群分”．下面将圆锥曲线分为抛物线、椭圆（圆）和双曲线三种情形，借用判别式法对定理给出如下证明． 定理1已知点和直线是抛物线的一对极点与极线．则（1）点在上直线与相切于点；（2）点 在内直线与相离；（3）点在外直线与 相交． 证明由得，，将其代入抛物线方程得， ，所以．所以，（1）点在上 直线与相切于点；（2）点在内 直线与相离；（3）点在外 直线与相交． 定理2已知点和直线是椭圆（圆） 的一对极点与极线．则（1）点在上
重要极限的证明
1.求证：sin(π/(2n+1))sin(2π/(2n+1))sin(3π/(2n+1))……sin(nπ /(2n+1))=√(2n +1)/2^n, Sol:复数方法： 复数方程 z^(2n＋1)＝1的根是 a1，a2，a3，...，a(2n)，1。 其中，ak＝cos(2kπ/(2n+1))＋i sin(2kπ/(2n+1))，k＝1，2，...，2n。 所以，ak＝(a1)^k 所以，z^(2n＋1)－1＝(z－a1)(z－a2)...(z－a(2n))(z－1)，即 (z－a1)(z－a2)...(z－a(2n))＝(z^(2n＋1)－1)/(z－1)＝z^(2n)＋z^(2n－1)＋...＋z＋1。 两边令z＝1，并取模，则： |1－a1|×|1－a2|×......×|1－a2n|＝2n＋1.........（*) 因为，|1－ak|＝√|(cos(2kπ/(2n+1))－1))＋i sin(2kπ/(2n+1))|＝2× sin(kπ/(2n+1))，所以由(*)式得： 2^n×sin(π/(2n+1))sin(2π/(2n+1))sin(3π/(2n+1))……sin(nπ/(2n+1)) ＝2n＋1。 所以，sin(π/(2n+1))sin(2π/(2n+1))sin(3π/(2n+1))……sin(nπ/(2n+1))＝√(2n＋1)/2^n 2.三角函数 求证：sin(π/(2n+1))sin(2π/(2n+1))sin(3π/(2n+1))……sin(nπ /(2n+1))=√(2n +1)/2^n. 证:sin(π/(2n+1))sin(2π/(2n+1))sin(3π/(2n+1))........sin(nπ /(2n+1))=√(2n +1)/2^n 设Z=cos2π/(2n+1)+ isin2π/(2n+1) 则x^(2n+1)=1的根为1,z,...z^2n 得x^2n+...+x+1=(x-z)(x-z^2)...(x-z^2n) 2n+1=｜(1-z)｜｜(1-z^2)｜...｜(1-z^2n)｜ (1) 又｜(1-z^k)｜=2sinkπ/(2n+1) (2) |1-z^k| = |1-(cos(2kπ/(2n+1)) +sin(2kπ/(2n+1)) )| =|1-cos(2kπ/(2n+1))) -sin(2kπ/(2n+1)) )| =√((1-2cos(2kπ/(2n+1)) +cos^2 (2kπ/(2n+1))) + sin^2 (2kπ/(2n+1))) =√(2-2cos(2kπ/(2n+1)) ) =√(4sin^2(kπ/(2n+1)) =2sin(kπ/(2n+1) 故 2n+1 =( n(π/(2n+1)). n(2π/(2n+1)) n(3π/(2n+1))........ n(2nπ/(2n+1)) 两边开方,得 sin(π/(2n+1))sin(2π/(2n+1))sin(3π/(2n+1))........sin(nπ/(2n+1)) =√(2n+1) / 2^n 另外那个类似,可以尝试自己证一下. 3.为什么sinπ／n+sin2π／n......+sin(n-1)π／n=cotπ／2n?
两个重要极限的证明
两个重要极限的证明第六节极限存在准则、两个重要极限 教学目的：1 使学生掌握极限存在的两个准则；并会利用它们求极限； 2使学生掌握利用两个重要极限求极限的方法； 教学重点：利用两个重要极限求极限 教学过程： 一、讲授新课： 准则I：如果数列满足下列条件： (i)对 ; (ii) 那么，数列的极限存在，且。 证明：因为，所以对，当时，有，即 ，对，当时，有，即，又因为，所以当时，有， 即有：，即，所以。 准则I′如果函数满足下列条件： (i)当时，有。 (ii)当时，有。 那么当时，的极限存在，且等于。 第一个重要极限： 作为准则I′的应用，下面将证明第一个重要极限：。 证明：作单位圆，如下图： 设为圆心角，并设见图不难发现：，即：，即， (因为，所以上不等式不改变方向) 当改变符号时，及1的值均不变，故对满足的一切 ，有。 又因为， 所以而，证毕。 【例1】。 【例2】。 【例3】。 【例4】。 准则Ⅱ：单调有界数列必有极限 如果数列满足：，就称之为单调增加数列;若满足：，就称之为单调减少数列;同理亦有严格单增或单减，以上通称为单减数列和严格单减数列。 如果，使得：，就称数列为有上界;若，使得：，就称有下界。 准则Ⅱ′：单调上升，且有上界的数列必有极限。 准则Ⅱ″: 单调下降，且有下界的数列必有极限。 注1：由前已知，有界数列未必有极限，若加单调性，就有极限。 2：准则Ⅱ，Ⅱ′，Ⅱ″可推广到函数情形中去，在此不一一陈述了。 第二个重要极限： 作为准则Ⅱ的一个应用，下面来证明极限是不存在的。 先考虑取正整数时的情形：对于，有不等式：，即：， 即： (i)现令，显然，因为将其代入，所以，所以为单调数列。 (ii)又令，所以， 即对，又对所以{ }是有界的。 由准则Ⅱ或Ⅱ′知存在，并使用来表示，即
两个重要极限的证明
两个重要的极限 1．证明：0sin lim 1x x x →= 证明：如图（a ）作单位圆。当0 重要极限的证明 重要极限的证明极限是ea0在n比较大时，(1 (1-a)/n)^n=原式=(1 1/n)^n取极限后，e》=原式的上极限》=原式的下极限》=e^(1-a)由a的任意性，得极限为e利用极限存在准则证明：(1)当x趋近于正无穷时，(Inx/x^2)的极限为0;(2)证明数列{Xn}，其中a0，Xo0,Xn=[(Xn-1) (a/Xn-1)]/2,n=1,2,…收敛，并求其极限。1)用夹逼准则:x大于1时,lnx0,x^20,故lnx/x^20且lnx1),lnx/x^2(x-1)/x^2.而(x-1)/x^2极限为0故(Inx/x^2)的极限为02)用单调有界数列收敛:分三种情况,x0=√a时,显然极限为√ax0√a时,Xn-X(n-1)=[-(Xn-1) (a/Xn-1)]/20,单调递减且Xn=[(Xn-1) (a/Xn-1)]/2√a,√a为数列下界,则极限存在.设数列极限为A,Xn和X(n-1)极限都为A.对原始两边求极限得A=[A (a/A)]/2.解得A=√a同理可求x0√a时,极限亦为√a综上,数列极限存在,且为√(一)时函数的极限：以时和为例引入.介绍符号: 的意义, 的直观意义.定义( 和. )几何意义介绍邻域其中为充分大的正数.然后用这些邻域语言介绍几何意义.例1验证例2验证例3验证证……(二)时函数的极限：由考虑时的极限引入.定义函数极限的“ ”定义.几何意义.用定义验证函数极限的基本思路.例4 验证例5 验证例6验证证由=为使需有为使需有于是, 倘限制, 就有例7验证例8验证( 类似有(三)单侧极限:1.定义：单侧极限的定义及记法.几何意义: 介绍半邻域然后介绍等的几何意义.例9验证证考虑使的2.单侧极限与双侧极限的关系:Th类似有: 例10证明: 极限不存在.例11设函数在点的某邻域内单调. 若存在, 则有= §2 函数极限的性质(3学时)教学目的：使学生掌握函数极限的基本性质。教学要求：掌握函数极限的基本性质：唯一性、局部保号性、不等式性质以及有理运算性等。教学重点：函数极限的性质及其计算。教学难点：函数极限性质证明及其应用。教学方法：讲练结合。一、组织教学：我们引进了六种极限: , .以下以极限为例讨论性质. 均给出证明或简证.二、讲授新课：(一)函数极限的性质:以下性质均以定理形式给出.1.唯一性:2.局部有界性:3.局部保号性:4.单调性( 不等式性质):Th 4若和都存在, 且存在点的空心邻域,使，都有证设= ( 现证对有)註:若在Th 4的条件中, 改“ ”为“ ”, 未必就有以举例说明.5.迫敛性:6.四则运算性质:( 只证“ ”和“ ”)(二)利用极限性质求极限：已证明过以下几个极限：(注意前四个极限中极限就是函数值)这些极限可作为公式用. 在计算一些简单极限时, 有五组基本极限作为公式用,我们将陆续证明这些公式.利用极限性质，特别是运算性质求极限的原理是：通过有关性质, 把所求极限化为基本极限,代入基本极限的值, 即计算得所求极限.例1( 利用极限和)例2例3註:关于的有理分式当时的极限.例4 [ 利用公式]例5例6例7 两个重要的极限的证明 引言： 两个重要极限是高等数学极限理论中的经典内容，第一个重要极限0sin lim 1x x x →=的证明，现行教材中 通常采用在单位圆中利用面积关系构造不等式sin cos 1x x x < <，再用夹逼原理证明得到结论。用极限理论计算圆或扇形面积都涉及到0sin lim 1x x x →=的结论运用，或者运洛比达法则证明极限0sin lim 1x x x →=，要利 用导数公式()sin cos x x '=，而这个公式恰是利用0sin lim 1x x x →=，因此，这些方法都有循环证明的嫌疑； 第二个主要极限01lim x x x e x →? ?+= ???的证明，通常作法是，先考虑x 取正整数n 而趋于+∞的情形，设 1n n x x n ? ?=+ ?? ?，用牛顿二项式证明{}n x 单调有界，再用单调有界数列必有极限的准则，证明数列{}n x 的 极限存在，方法比较复杂，特别是有界性的证明需要一定的技巧，所以本文只对两个重要极限作一个简单 的证明。 1．证明：0sin lim 1x x x →= 证明：如图（a ）作单位圆。当0 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 强度极限/N 屈服极限/N 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68093.040855.890790.754474.490790.772632.6113488.468093.0113488.490790.7136186.0108948.8181581.4145265.1204279.1163423.3226976.7181581.4272372.1245134.9拉力117120.070272.0156160.093696.0156160.0124928.0195200.0117120.0195200.0156160.0234240.0187392.0312320.0249856.0351360.0281088.0390400.0312320.0468480.0421632.0剪切力117120.070272.0156160.093696.0156160.0124928.0195200.0117120.0195200.0156160.0234240.0187392.0312320.0249856.0351360.0281088.0390400.0312320.0468480.0421632.0拉力68093.040855.890790.754474.490790.772632.6113488.468093.0113488.490790.7136186.0108948.8181581.4145265.1204279.1163423.3226976.7181581.4272372.1245134.9剪切力68093.040855.890790.754474.490790.772632.6113488.468093.0113488.490790.7136186.0108948.8 181581.4 145265.1204279.1163423.3226976.7181581.4272372.1245134.9 常用螺栓强度/屈服极限一览表 353 螺栓规格 螺栓型号应力截面积 工况受力形式 3.6 4.6 4.8 5.6 5.8 6.88.8（D<=M16)8.8（D>M16)9.810.8M1 M2 M3 0.46 M14 2.07 5.03 115 157 192 245 303 12.9 性能等级 动载荷不控制预紧力 控制预紧力 不控制预紧力 静载荷 动载荷静载荷 动载荷 静载荷 静载荷 动载荷 静载荷 动载荷静载荷 动载荷 控制预紧力 不控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 M33 M36 M39 M24 M27 M30 M4 M5 M6 M8 M10 M12 M16 M18 M20 M22 不控制预紧力 控制预紧力 459 561 694 8.78 14.2 20.1 36.6 58 84.3 不控制预紧力 控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 不控制预紧力 控制预紧力 动载荷 静载荷 动载荷静载荷 动载荷 静载荷 动载荷 静载荷 动载荷静载荷 动载荷 静载荷 动载荷静载荷 动载荷静载荷 动载荷 静载荷 动载荷静载荷 动载荷静载荷 动载荷 静载荷 静载荷 动载荷 静载荷 动载荷静载荷 动载荷 静载荷 动载荷静载荷 动载荷 静载荷 动载荷动载荷 静载荷 动载荷静载荷 动载荷 静载荷 动载荷静载荷 静载荷 动载荷 静载荷 动载荷动载荷 静载荷 动载荷静载荷 静载荷 动载荷 静载荷 动载荷静载荷 动载荷 静载荷 动载荷 在本表的计算中，当D重要极限的证明_1
两个极限的简单证明
常用螺栓强度极限 屈服极限一览表