PKSxTńB–Hmimetypetext/x-wxmathmlPKSxTQdBV55 format.txt This file contains a wxMaxima session in the .wxmx format. .wxmx files are .xml-based files contained in a .zip container like .odt or .docx files. After changing their name to end in .zip the .xml and eventual bitmap files inside them can be extracted using any .zip file viewer. The reason why part of a .wxmx file still might still seem to make sense in a ordinary text viewer is that the text portion of .wxmx by default isn't compressed: The text is typically small and compressing it would mean that changing a single character would (with a high probability) change big parts of the whole contents of the compressed .zip archive. Even if version control tools like git and svn that remember all changes that were ever made to a file can handle binary files compression would make the changed part of the file bigger and therefore seriously reduce the efficiency of version control wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima. It also is part of the windows installer for maxima (https://wxmaxima-developers.github.io/wxmaxima/). If a .wxmx file is broken but the content.xml portion of the file can still be viewed using an text editor just save the xml's text as "content.xml" and try to open it using a recent version of wxMaxima. If it is valid XML (the XML header is intact, all opened tags are closed again, the text is saved with the text encoding "UTF8 without BOM" and the few special characters XML requires this for are properly escaped) chances are high that wxMaxima will be able to recover all code and text from the XML file. PKSxTń=r9r9 content.xml Kedvenc Matematikai KĂ­sĂ©rleteim Alapok Halmazok Ă©s fĂŒggvĂ©nyek SzĂĄmok HatĂĄrĂ©rtĂ©k DifferenciĂĄlszĂĄmĂ­tĂĄs IntegrĂĄlszĂĄmĂ­tĂĄs LineĂĄris algrebra TöbbvĂĄltozĂłs fĂŒggvĂ©nyek MĂ©rtĂ©k Ă©s valĂłszĂ­nƱsĂ©g MĂ©rtĂ©k IntegrĂĄl DefinĂ­ciĂł A nemnegatĂ­v fĂŒggvĂ©nyek integrĂĄljĂĄnak tulajdonsĂĄgai Beppo Levi tĂ©tele Fatou-lemma NemnegatĂ­v mĂ©rhetƑ fĂŒggvĂ©nyek integrĂĄljĂĄnak megszĂĄmlĂĄlhatĂł additivitĂĄsa IntegrĂĄlhatĂł fĂŒggvĂ©nyek BƑvĂ­tett valĂłs Ă©rtĂ©kƱ fĂŒggvĂ©nyek integrĂĄljĂĄnak tulajdonsĂĄgai Komplex Ă©s vektor Ă©rtĂ©kƱ fĂŒggvĂ©nyek integrĂĄlja MegjegyzĂ©s Lebesgue tĂ©tele Az integrĂĄl abszolĂșt folytonossĂĄga Az integrĂĄl σ-additivitĂĄsa A Kurzweil-fĂ©le Ă©s a Lebesgue-integrĂĄl Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat MĂ©rtĂ©kterek szorzata Fubini-tĂ©tel Feladat Feladat Feladat kill(all); (%o0) done (1) assume(x>0,y>0); (%o1) [x>0,y>0] integrate((x^2-y^2)/(x^2+y^2)^2,x,0,1); (%o2) −1y2+1 integrate(%,y,0,1); (%o3) −%pi4 A mĂĄsodik az ellentettje, a mĂĄsik kettƑ vĂ©gtelen; (2) kill(all); (%o0) done assume(y>0,y<1/2); (%o1) [y>0,y<12] integrate(1/(x-1/2)^3,x,0,1/2-y); (%o2) 2−12*y2 integrate(1/(x-1/2)^3,x,1/2+y,1); (%o3) 12*y2−2 Az elsƑ integrĂĄl nulla, a harmadik viszont plusz vĂ©gtelen: integrate(1/y^2-4,y,0,1/2); defint: integral is divergent. -- an error. To debug this try: debugmode(true); MĂĄsrĂ©szt integrate(1/(x-1/2)^3,y,0,1/2-x); (%o4) 12−x

x−12

3 integrate(1/(x-1/2)^3,y,0,x-1/2); (%o5) 1

x−12

2 ÖsszegĂŒk nulla, Ă­gy a mĂĄsodik integrĂĄl is nulla. Viszont az abszolĂșt Ă©rtĂ©keket integrĂĄlva az integrĂĄl vĂ©gtelen: integrate(2/(x-1/2)^2,x,0,1); defint: integral is divergent. -- an error. To debug this try: debugmode(true); (3) integrate((x-y)/(x^2+y^2)/(3/2),x,0,1); (%o4) 2*

log

y2+1

2−log

y

−atan

1y

3 integrate(%,y,0,1); (%o5) 0 A mĂĄsodik is nulla, de a harmadik Ă©s a negyedik vĂ©gtelen: polĂĄr koordinĂĄtĂĄkra ĂĄttĂ©rve, Ă©s csak π/6-ig integrĂĄlva, c*r/r^3-öt kell integrĂĄlni, ahol c>0. (4) MindenĂŒtt pozitĂ­v, Ă­gy az integrĂĄlok egyenlƑek. VezessĂŒnk be Ășj vĂĄltozĂłkat, u:x*y, v:y/x, 0<u<1, 0<v<infty kill(all); (%o0) done assume(u>0,v>0); (%o1) [u>0,v>0] x:sqrt(u/v); (%o2) uv y:sqrt(u*v); (%o3) u*v jacobian([x,y],[u,v]); (%o9) 12*u*v−u2*v32v2*uu2*v determinant(%); (%o10) 12*v Mivel 1/v integrĂĄlja vĂ©gtelen, (1-u)^(-p) integrĂĄlja meg pozitĂ­v, az integrĂĄl mindig vĂ©gtelen. Feladat: az integrĂĄl, mint görbe alatti terĂŒlet Feladat EloszlĂĄsfĂŒggvĂ©ny IntegrĂĄl Ă©s eloszlĂĄsfĂŒggvĂ©ny PKSxTńB–HmimetypePKSxTQdBV55 5format.txtPKSxTń=r9r9 ’content.xmlPK§-@