<?xml version="1.0" encoding="utf-8" ?><rss version="2.0"><channel><title><![CDATA[qq_45491237的博客]]></title><description><![CDATA[]]></description><link>https://blog.youkuaiyun.com/qq_45491237</link><language>zh-cn</language><generator>https://blog.youkuaiyun.com/</generator><copyright><![CDATA[Copyright &copy; qq_45491237]]></copyright><item><title><![CDATA[积分学＜6＞——反常积分]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/137793067</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/137793067</guid><author>qq_45491237</author><pubDate>Mon, 15 Apr 2024 20:47:01 +0800</pubDate><description><![CDATA[若函数fxfx在区间a∞a∞a∈Ra∈R)上有定义,且∀Aa∀Aa若函数fxfx在aAaA上可积,构造变上限积分FA∫aAfxdxFA∫aA​fxdx若极限lim⁡A→∞FAlim⁡A→∞∫aAfxdxF∞−FalimA→∞​FAlimA→∞​∫aA​fxdxF∞−Fa存在且有限,则称反常积分∫a∞f。]]></description><category></category></item><item><title><![CDATA[积分学＜5＞——微积分基本定理]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/137748856</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/137748856</guid><author>qq_45491237</author><pubDate>Sun, 14 Apr 2024 18:57:37 +0800</pubDate><description><![CDATA[函数Fx∫axftdtFx∫ax​ftdt称为变上限积分,x∈abx∈ab为自变量,ttt为参数。]]></description><category></category></item><item><title><![CDATA[积分学＜4＞——定积分的性质]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/137677386</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/137677386</guid><author>qq_45491237</author><pubDate>Sun, 14 Apr 2024 16:53:08 +0800</pubDate><description><![CDATA[上可积,则可取一个划分P,设c为P的一个分点x_{k}(如不然,将c作为新分点添加入划分P,根据引理3.1,取一个包含分点c=x_{r}的划分P,设在闭区间。根据定积分的保序性和线性性,根据定积分的线性性,函数。根据数列极限的保序性,上均可积,反之亦然,且。]]></description><category></category></item><item><title><![CDATA[积分学＜3＞——定积分与可积条件]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/137606008</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/137606008</guid><author>qq_45491237</author><pubDate>Thu, 11 Apr 2024 21:31:59 +0800</pubDate><description><![CDATA[若函数fxfx是闭区间abab上的有界函数,对闭区间abab作划分Pxi−1xi∣x0a≤xi−1xi≤xnb1≤i≤ni∈NPxi−1​xi​∣x0​a≤xi−1​xi​≤xn​b1≤i≤ni∈N,也就是选取包含闭区间abab左端点a和右端点b在内的n1n+1n1个点xix_{i}xi​将闭区间abab分为n−1。]]></description><category></category></item><item><title><![CDATA[积分学＜2＞——换元积分法和分部积分法]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/137566807</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/137566807</guid><author>qq_45491237</author><pubDate>Wed, 10 Apr 2024 13:54:49 +0800</pubDate><description><![CDATA[若fxf​xg′x,且∫f​uduFuC,则∫fxdxFgxC。Fgx′F′gx⋅g′xf​gxg′xfx。xφt,且反函数φ−1xt存在,则∫fxdx∫fφtφ′tdtFφ−1xC。Fφ−1x′φ′tF′φ−1x​φ′tfφtφ′t​fφtfx。fxuxvx,dfxuxdv。]]></description><category></category></item><item><title><![CDATA[积分学＜1＞——不定积分]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/137550356</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/137550356</guid><author>qq_45491237</author><pubDate>Tue, 09 Apr 2024 20:09:04 +0800</pubDate><description><![CDATA[若函数f\left ( x \right )在区间X上有定义,且F^{\prime } \left ( x \right ) =f\left ( x \right ),则称F\left ( x \right )为f\left ( x \right )的一个原函数。]]></description><category></category></item><item><title><![CDATA[微分学＜6＞——Taylor公式]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/136882166</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/136882166</guid><author>qq_45491237</author><pubDate>Thu, 21 Mar 2024 02:51:01 +0800</pubDate><description><![CDATA[时,Taylor公式表现为Lagrange中值定理的形式。连续引用n-1次L’Hospital法则,在Taylor近似时产生的误差,余下的。,其中Lagrange余项。引用Cauchy中值定理,阶导数均存在,则存在邻域。阶导函数一定连续且可导。次Taylor多项式。阶连续导数,在开区间。]]></description><category></category></item><item><title><![CDATA[微分学＜5＞——L‘Hopital法则]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/136588833</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/136588833</guid><author>qq_45491237</author><pubDate>Wed, 20 Mar 2024 00:04:22 +0800</pubDate><description><![CDATA[L’Hopital法则同样适用于。根据数列极限的定理2.1,根据数列极限的定理2.1,根据Cauchy中值定理,根据Cauchy中值定理,根据函数极限的局部保序性,引用函数极限的局部保号性,根据Cauchy中值定理,根据函数极限的局部保序性,引用函数极限的局部保号性,以"0"代表无穷小量,"直接应用的结论,]]></description><category></category></item><item><title><![CDATA[微分学＜4＞——微分中值定理]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/136568218</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/136568218</guid><author>qq_45491237</author><pubDate>Sat, 09 Mar 2024 18:52:25 +0800</pubDate><description><![CDATA[若存在x0x_{0}x0​的邻域Ux0δUx0​δ,使得∀x∈Ux0δ∀x∈Ux0​δfx≤fx0fx≤fx0​,则称x0x_{0}x0​是函数fxfx的一个极大值点。若存在x0x_{0}x0​的邻域Ux0δUx0​δ,使得∀x∈Ux0δ∀x∈Ux0​δfx≥fx0fx≥fx0​,则称x0x_{0}x0​。]]></description><category></category></item><item><title><![CDATA[微分学＜3＞——高阶导数]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/136478922</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/136478922</guid><author>qq_45491237</author><pubDate>Fri, 08 Mar 2024 17:38:03 +0800</pubDate><description><![CDATA[若yfxyfx的前n−1n-1n−1阶导函数均存在,且第n−1n-1n−1阶导函数可导,则将fxfx的第n−1n-1n−1阶导函数的求导产物称为fxfx的nnn阶导函数,记作fn−1x′fnxfn−1x′fnx或dnydxndnydxndxndny​dxndny​dnfdxndnfdxndxndnf​dxnd。]]></description><category></category></item><item><title><![CDATA[微分学＜2＞——导数的定义与求导法则]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/136378467</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/136378467</guid><author>qq_45491237</author><pubDate>Tue, 05 Mar 2024 14:52:05 +0800</pubDate><description><![CDATA[若yfxyfx可微,则当Δx→0Δx→0时,有lim⁡Δx→0ΔyΔxlim⁡Δx→0fx△x−fxΔxlimΔx→0​ΔxΔy​limΔx→0​Δxfx+△x−fx​存在,则称函数yfxyfx可导,称lim⁡Δx→0ΔyΔxlimΔx→0​ΔxΔy​为fxfx的导函数f′xdydxdfdxf。]]></description><category></category></item><item><title><![CDATA[微分学＜1＞——微分]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/136283265</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/136283265</guid><author>qq_45491237</author><pubDate>Thu, 29 Feb 2024 18:52:06 +0800</pubDate><description><![CDATA[若yfxyfxx0∈Dfx0​∈Df​∃gx0∃gx0​∀ΔxΔx→0∀ΔxΔx→0Δygx0ΔxoΔxΔygx0​ΔxoΔx,此时称yfxyfx在x0x_{0}x0​处可微,若yfxyfx在区间XXX每一点上处处可微,则称yfxyfx在区间XXX上可微。其中gx0Δxgx0​Δx称为微分的线性主要部分。]]></description><category></category></item><item><title><![CDATA[函数极限＜5＞——闭区间上的连续函数]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/135756080</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/135756080</guid><author>qq_45491237</author><pubDate>Wed, 21 Feb 2024 22:16:15 +0800</pubDate><description><![CDATA[若函数fxfx在区间XXX上有定义,且∀ε0∀ε0∃δ0∃δ0∀x′∀x′x′′x′′∣x′−x′′∣δ∣x′−x′′∣δ∣fx′−fx′′∣ε∣fx′−fx′′∣ε,则称函数fxfx在区间XXX上一致连续。]]></description><category></category></item><item><title><![CDATA[函数极限＜4＞——无穷小量的阶]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/135611033</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/135611033</guid><author>qq_45491237</author><pubDate>Sun, 21 Jan 2024 19:45:28 +0800</pubDate><description><![CDATA[若lim⁡x→x0uxvx0limx→x0​​vxux​0,则称当x→x0x\to x_{0}x→x0​时,uxux是vxvx的高阶无穷小量,记为uxovxuxovx,相对的,当x→x0x\to x_{0}x→x0​时,vxvx是uxux的低阶无穷小量。若在x0x_{0}x0​的某一去心邻域内,∣uxvx∣≤AA∈R​vxux​。]]></description><category></category></item><item><title><![CDATA[函数极限＜3＞——连续函数]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/135279523</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/135279523</guid><author>qq_45491237</author><pubDate>Wed, 10 Jan 2024 12:09:41 +0800</pubDate><description><![CDATA[若函数fx在邻域U˚x0δf\left ( x \right )在邻域\mathring{U} \left ( x_{0},\delta  \right )fx在邻域U˚x0​δ上有定义,且∀ε0∀ε0∃δ0∃δ0∀x∣x−x0∣δ∀x∣x−x0​∣δ∣fx−fx0∣ε∣fx−fx0​∣ε,也就是lim⁡x→x0fxfx0limx→x0​​。]]></description><category></category></item><item><title><![CDATA[函数极限＜2＞——Heine定理]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/135259496</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/135259496</guid><author>qq_45491237</author><pubDate>Thu, 28 Dec 2023 05:18:07 +0800</pubDate><description><![CDATA[可以直接运用的结论证明。的充要条件是对任意满足。又根据函数极限定义,]]></description><category></category></item><item><title><![CDATA[函数极限＜1＞——函数极限]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/134917321</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/134917321</guid><author>qq_45491237</author><pubDate>Thu, 28 Dec 2023 05:05:40 +0800</pubDate><description><![CDATA[若函数fxfx在去心邻域U˚x0δU˚x0​δ内有定义,∀ε0∀ε0∃δ0∃δ0∀x0∣x−x0∣δ∀x0∣x−x0​∣δ∣fx−A∣ε∣fx−A∣ε,则称函数fxfx以实数AAA为极限,或函数fxfx收敛于极限AAA,符号化表述为lim⁡x→x0fxAlimx→x0​​fxA或fx→Ax→x0fx→。]]></description><category></category></item><item><title><![CDATA[数列极限＜3＞——实数系基本定理]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/134867259</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/134867259</guid><author>qq_45491237</author><pubDate>Sat, 09 Dec 2023 08:37:53 +0800</pubDate><description><![CDATA[设集合SSS为非空有限实数集,若∃m∈S∀x∈S∃m∈S∀x∈Sx≥mx\ge mx≥m,则称mmm为SSS的最小数,记为mmax⁡Sm =\max  SmmaxS。设集合SSS为非空有限实数集,若∃M∈S∀x∈S∃M∈S∀x∈Sx≤Mx\le Mx≤M,则称mmm为SSS的最大数,记为Mmin⁡SM =\min SMminS。设集合SSS为非空有限实数集,若。]]></description><category></category></item><item><title><![CDATA[数列极限＜2＞——无穷大量]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/134772878</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/134772878</guid><author>qq_45491237</author><pubDate>Mon, 04 Dec 2023 18:57:04 +0800</pubDate><description><![CDATA[若数列xnxn​∀G0∀G0∃N∀nN∃N∀nNxnGx_{n}>Gxn​G,则称xnxn​为正无穷大量;若数列xnxn​∀G0∀G0∃N∀nN∃N∀nNxn−Gx_{n}]]></description><category></category></item><item><title><![CDATA[数列极限＜1＞——数列极限]]></title><link>https://blog.youkuaiyun.com/qq_45491237/article/details/134647957</link><guid>https://blog.youkuaiyun.com/qq_45491237/article/details/134647957</guid><author>qq_45491237</author><pubDate>Sat, 02 Dec 2023 03:03:56 +0800</pubDate><description><![CDATA[实数轴上的点x0x_{0}x0​附近的开区间Ux0δx0−δx0δUx0​δx0​−δx0​δ称为x0x_{0}x0​的邻域,若不包含x0x_{0}x0​,则称为去心邻域Ux0δ−x0Ux0​δ−x0​。xnxn​∀ε0∀ε0∃N\exists N∃N∀nN∀nN∣xn−a∣ε∣xn​−a∣ε则称为数列xnxn​。]]></description><category></category></item></channel></rss>