Lösung Funktionsterme aus Eigenschaften
Analyse:
Es soll erkannt werden, dass ein beliebiger Funktionsterm gesucht wird, welche folgende Eigenschaften erfüllt: An der Stelle 2 und 4 soll der Term denselben y-Wert haben. An der Stelle 3 soll das Schaubild die Steigung 0 haben (Extrempunkt oder Sattelpunkt). Darüber hinaus soll die Steigung an der Stelle 2 etwa 4,7 betragen.
Das Integral über den Funktionsterm von 0 bis 4 muss einen größeren oder gleich großen Wert ergeben als das Integral über den Funktionsterm von 0 bis 1. Der Wert des Integrals von 0 bis 1 muss größer als der Wert des Integrals von 0 bis 2 sein, d. h. der Funktionsterm muss in [0;4] teilweise unter der x-Achse liegen.
Durchführung:
Mögliche Strategie: Anfertigen einer Skizze, welche die geforderten Eigenschaften erfüllt und bestimmen des Funktionsterms durch einen geeigneten Ansatz oder mittels Regression. Alternativ kann auch ein Ansatz ohne vorheriges skizzieren durch probieren versucht werden.
Möglicher Funktionsterm 1: Das Makro [formula] konnte nicht ausgeführt werden. Grund: [The image type [image/svg+xml] is not supported by the SnuggleTeX formula renderer.]. Klicke auf diese Nachricht, um Details zu erfahren.
org.xwiki.rendering.macro.MacroExecutionException: Failed to render formula [f
=-3sin(\frac{%pi}{2}x) ] using the [snuggletex] renderer
at org.xwiki.rendering.internal.macro.formula.FormulaMacro.render(FormulaMacro.java:173)
at org.xwiki.rendering.internal.macro.formula.FormulaMacro.execute(FormulaMacro.java:123)
at org.xwiki.rendering.internal.macro.formula.FormulaMacro.execute(FormulaMacro.java:60)
at org.xwiki.rendering.internal.transformation.macro.MacroTransformation.transform(MacroTransformation.java:311)
at org.xwiki.rendering.internal.transformation.DefaultRenderingContext.transformInContext(DefaultRenderingContext.java:183)
at org.xwiki.rendering.internal.transformation.DefaultTransformationManager.performTransformations(DefaultTransformationManager.java:88)
at org.xwiki.display.internal.DocumentContentAsyncExecutor.executeInCurrentExecutionContext(DocumentContentAsyncExecutor.java:396)
at org.xwiki.display.internal.DocumentContentAsyncExecutor.execute(DocumentContentAsyncExecutor.java:269)
at org.xwiki.display.internal.DocumentContentAsyncRenderer.execute(DocumentContentAsyncRenderer.java:112)
at org.xwiki.rendering.async.internal.block.AbstractBlockAsyncRenderer.render(AbstractBlockAsyncRenderer.java:157)
at org.xwiki.rendering.async.internal.block.AbstractBlockAsyncRenderer.render(AbstractBlockAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:290)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.execute(DefaultBlockAsyncRendererExecutor.java:125)
at org.xwiki.display.internal.DocumentContentDisplayer.display(DocumentContentDisplayer.java:67)
at org.xwiki.display.internal.DocumentContentDisplayer.display(DocumentContentDisplayer.java:43)
at org.xwiki.display.internal.DefaultDocumentDisplayer.display(DefaultDocumentDisplayer.java:96)
at org.xwiki.display.internal.DefaultDocumentDisplayer.display(DefaultDocumentDisplayer.java:39)
at org.xwiki.sheet.internal.SheetDocumentDisplayer.display(SheetDocumentDisplayer.java:123)
at org.xwiki.sheet.internal.SheetDocumentDisplayer.display(SheetDocumentDisplayer.java:52)
at org.xwiki.display.internal.ConfiguredDocumentDisplayer.display(ConfiguredDocumentDisplayer.java:68)
at org.xwiki.display.internal.ConfiguredDocumentDisplayer.display(ConfiguredDocumentDisplayer.java:42)
at com.xpn.xwiki.doc.XWikiDocument.display(XWikiDocument.java:1407)
at com.xpn.xwiki.doc.XWikiDocument.getRenderedContent(XWikiDocument.java:1543)
at com.xpn.xwiki.doc.XWikiDocument.displayDocument(XWikiDocument.java:1493)
at com.xpn.xwiki.doc.XWikiDocument.displayDocument(XWikiDocument.java:1462)
at com.xpn.xwiki.api.Document.displayDocument(Document.java:821)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
at java.base/java.lang.reflect.Method.invoke(Method.java:577)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.doInvoke(UberspectImpl.java:571)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.invoke(UberspectImpl.java:554)
at org.apache.velocity.runtime.parser.node.ASTMethod.execute(ASTMethod.java:221)
at org.apache.velocity.runtime.parser.node.ASTReference.execute(ASTReference.java:368)
at org.apache.velocity.runtime.parser.node.ASTReference.value(ASTReference.java:704)
at org.apache.velocity.runtime.parser.node.ASTExpression.value(ASTExpression.java:75)
at org.apache.velocity.runtime.parser.node.ASTSetDirective.render(ASTSetDirective.java:242)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.runtime.parser.node.ASTIfStatement.render(ASTIfStatement.java:190)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.xwiki.velocity.internal.directive.TryCatchDirective.render(TryCatchDirective.java:86)
at org.apache.velocity.runtime.parser.node.ASTDirective.render(ASTDirective.java:304)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.Template.merge(Template.java:358)
at org.apache.velocity.Template.merge(Template.java:262)
at org.xwiki.velocity.internal.InternalVelocityEngine.evaluate(InternalVelocityEngine.java:233)
at com.xpn.xwiki.internal.template.VelocityTemplateEvaluator.evaluateContent(VelocityTemplateEvaluator.java:107)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.evaluateContent(TemplateAsyncRenderer.java:219)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.renderVelocity(TemplateAsyncRenderer.java:174)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:135)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.lambda$syncRender$0(DefaultAsyncRendererExecutor.java:284)
at com.xpn.xwiki.internal.security.authorization.DefaultAuthorExecutor.call(DefaultAuthorExecutor.java:98)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:284)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.render(DefaultBlockAsyncRendererExecutor.java:154)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:904)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:866)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:853)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:808)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:800)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:79)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:73)
at org.xwiki.template.script.TemplateScriptService.render(TemplateScriptService.java:54)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
at java.base/java.lang.reflect.Method.invoke(Method.java:577)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.doInvoke(UberspectImpl.java:571)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.invoke(UberspectImpl.java:554)
at org.apache.velocity.runtime.parser.node.ASTMethod.execute(ASTMethod.java:221)
at org.apache.velocity.runtime.parser.node.ASTReference.execute(ASTReference.java:368)
at org.apache.velocity.runtime.parser.node.ASTReference.render(ASTReference.java:492)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.directive.VelocimacroProxy.render(VelocimacroProxy.java:217)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:331)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:261)
at org.apache.velocity.runtime.parser.node.ASTDirective.render(ASTDirective.java:304)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.Template.merge(Template.java:358)
at org.apache.velocity.Template.merge(Template.java:262)
at org.xwiki.velocity.internal.InternalVelocityEngine.evaluate(InternalVelocityEngine.java:233)
at com.xpn.xwiki.internal.template.VelocityTemplateEvaluator.evaluateContent(VelocityTemplateEvaluator.java:107)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.evaluateContent(TemplateAsyncRenderer.java:219)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.renderVelocity(TemplateAsyncRenderer.java:174)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:135)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.lambda$syncRender$0(DefaultAsyncRendererExecutor.java:284)
at com.xpn.xwiki.internal.security.authorization.DefaultAuthorExecutor.call(DefaultAuthorExecutor.java:98)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:284)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.render(DefaultBlockAsyncRendererExecutor.java:154)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:904)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:866)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:853)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:808)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:800)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:79)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:73)
at org.xwiki.template.script.TemplateScriptService.render(TemplateScriptService.java:54)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
at java.base/java.lang.reflect.Method.invoke(Method.java:577)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.doInvoke(UberspectImpl.java:571)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.invoke(UberspectImpl.java:554)
at org.apache.velocity.runtime.parser.node.ASTMethod.execute(ASTMethod.java:221)
at org.apache.velocity.runtime.parser.node.ASTReference.execute(ASTReference.java:368)
at org.apache.velocity.runtime.parser.node.ASTReference.render(ASTReference.java:492)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.directive.VelocimacroProxy.render(VelocimacroProxy.java:217)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:331)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:261)
at org.apache.velocity.runtime.parser.node.ASTDirective.render(ASTDirective.java:304)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.parser.node.ASTIfStatement.render(ASTIfStatement.java:171)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.runtime.parser.node.ASTIfStatement.render(ASTIfStatement.java:190)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.Template.merge(Template.java:358)
at org.apache.velocity.Template.merge(Template.java:262)
at org.xwiki.velocity.internal.InternalVelocityEngine.evaluate(InternalVelocityEngine.java:233)
at com.xpn.xwiki.internal.template.VelocityTemplateEvaluator.evaluateContent(VelocityTemplateEvaluator.java:107)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.evaluateContent(TemplateAsyncRenderer.java:219)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.renderVelocity(TemplateAsyncRenderer.java:174)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:135)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.lambda$syncRender$0(DefaultAsyncRendererExecutor.java:284)
at com.xpn.xwiki.internal.security.authorization.DefaultAuthorExecutor.call(DefaultAuthorExecutor.java:98)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:284)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.render(DefaultBlockAsyncRendererExecutor.java:154)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:904)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:866)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:846)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:832)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.render(DefaultTemplateManager.java:91)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.render(DefaultTemplateManager.java:85)
at com.xpn.xwiki.XWiki.evaluateTemplate(XWiki.java:2569)
at com.xpn.xwiki.web.Utils.parseTemplate(Utils.java:180)
at com.xpn.xwiki.web.XWikiAction.execute(XWikiAction.java:650)
at com.xpn.xwiki.web.XWikiAction.execute(XWikiAction.java:338)
at com.xpn.xwiki.web.LegacyActionServlet.service(LegacyActionServlet.java:108)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:764)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:227)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at com.xpn.xwiki.web.ActionFilter.doFilter(ActionFilter.java:122)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.wysiwyg.filter.ConversionFilter.doFilter(ConversionFilter.java:61)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:53)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.container.servlet.filters.internal.SetHTTPHeaderFilter.doFilter(SetHTTPHeaderFilter.java:63)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.resource.servlet.RoutingFilter.doFilter(RoutingFilter.java:132)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.container.servlet.filters.internal.SavedRequestRestorerFilter.doFilter(SavedRequestRestorerFilter.java:208)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.container.servlet.filters.internal.SetCharacterEncodingFilter.doFilter(SetCharacterEncodingFilter.java:117)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:197)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:97)
at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:540)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:135)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:92)
at org.apache.catalina.valves.AbstractAccessLogValve.invoke(AbstractAccessLogValve.java:687)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:78)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:359)
at org.apache.coyote.ajp.AjpProcessor.service(AjpProcessor.java:433)
at org.apache.coyote.AbstractProcessorLight.process(AbstractProcessorLight.java:65)
at org.apache.coyote.AbstractProtocol$ConnectionHandler.process(AbstractProtocol.java:889)
at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.doRun(NioEndpoint.java:1735)
at org.apache.tomcat.util.net.SocketProcessorBase.run(SocketProcessorBase.java:49)
at org.apache.tomcat.util.threads.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1191)
at org.apache.tomcat.util.threads.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:659)
at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
at java.base/java.lang.Thread.run(Thread.java:833)
Caused by: java.lang.IllegalArgumentException: The image type [image/svg+xml] is not supported by the SnuggleTeX formula renderer.
at org.xwiki.formula.internal.SnuggleTexFormulaRenderer.renderImage(SnuggleTexFormulaRenderer.java:76)
at org.xwiki.formula.AbstractFormulaRenderer.process(AbstractFormulaRenderer.java:55)
at org.xwiki.rendering.internal.macro.formula.FormulaMacro.render(FormulaMacro.java:161)
... 180 more
Hier könnte man erwarten, dass die Korrektheit der Bedingungen beim ermittelten Funktionsterm nachgerechnet werden.
Zum Beispiel für den möglichen Funktionsterm 1: