Hello java com Rest

Pessoal estou aprendendo a usar o rest, fiz da mesma forma que estava no tutorial mas toda vez que vou iniciar o servidor tomcat da esse erro.

INFORMAÇÕES: Starting Servlet Engine: Apache Tomcat/7.0.70
ago 03, 2016 9:55:12 AM org.apache.catalina.core.ContainerBase startInternal
GRAVE: A child container failed during start
java.util.concurrent.ExecutionException: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/HelloRest]]
     at java.util.concurrent.FutureTask.report(Unknown Source)
     at java.util.concurrent.FutureTask.get(Unknown Source)
     at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:1119)
     at org.apache.catalina.core.StandardHost.startInternal(StandardHost.java:819)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1571)
     at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1561)
     at java.util.concurrent.FutureTask.run(Unknown Source)
     at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
     at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
     at java.lang.Thread.run(Unknown Source)
 Caused by: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/HelloRest]]
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:153)
     ... 6 more
 Caused by: java.lang.IllegalArgumentException: Servlet mapping specifies an unknown servlet name javax.ws.rs.core.Application
     at org.apache.catalina.core.StandardContext.addServletMapping(StandardContext.java:3406)
     at org.apache.catalina.core.StandardContext.addServletMapping(StandardContext.java:3385)
     at org.apache.catalina.deploy.WebXml.configureContext(WebXml.java:1438)
     at org.apache.catalina.startup.ContextConfig.webConfig(ContextConfig.java:1355)
     at org.apache.catalina.startup.ContextConfig.configureStart(ContextConfig.java:887)
     at org.apache.catalina.startup.ContextConfig.lifecycleEvent(ContextConfig.java:387)
     at org.apache.catalina.util.LifecycleSupport.fireLifecycleEvent(LifecycleSupport.java:117)
     at org.apache.catalina.util.LifecycleBase.fireLifecycleEvent(LifecycleBase.java:90)
     at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5503)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     ... 6 more

 ago 03, 2016 9:55:12 AM org.apache.catalina.core.ContainerBase startInternal
 GRAVE: A child container failed during start
 java.util.concurrent.ExecutionException: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost]]
     at java.util.concurrent.FutureTask.report(Unknown Source)
     at java.util.concurrent.FutureTask.get(Unknown Source)
     at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:1119)
     at org.apache.catalina.core.StandardEngine.startInternal(StandardEngine.java:300)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     at org.apache.catalina.core.StandardService.startInternal(StandardService.java:444)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     at org.apache.catalina.core.StandardServer.startInternal(StandardServer.java:756)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     at org.apache.catalina.startup.Catalina.start(Catalina.java:693)
     at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
     at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
     at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
     at java.lang.reflect.Method.invoke(Unknown Source)
     at org.apache.catalina.startup.Bootstrap.start(Bootstrap.java:294)
     at org.apache.catalina.startup.Bootstrap.main(Bootstrap.java:428)
 Caused by: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost]]
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:153)
     at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1571)
     at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1561)
     at java.util.concurrent.FutureTask.run(Unknown Source)
     at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
     at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
     at java.lang.Thread.run(Unknown Source)
 Caused by: org.apache.catalina.LifecycleException: A child container failed during start
     at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:1127)
     at org.apache.catalina.core.StandardHost.startInternal(StandardHost.java:819)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     ... 6 more

 ago 03, 2016 9:55:12 AM org.apache.catalina.startup.Catalina start
 GRAVE: The required Server component failed to start so Tomcat is unable to start.
 org.apache.catalina.LifecycleException: Failed to start component [StandardServer[8005]]
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:153)
     at org.apache.catalina.startup.Catalina.start(Catalina.java:693)
     at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
     at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
     at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
     at java.lang.reflect.Method.invoke(Unknown Source)
     at org.apache.catalina.startup.Bootstrap.start(Bootstrap.java:294)
     at org.apache.catalina.startup.Bootstrap.main(Bootstrap.java:428)
 Caused by: org.apache.catalina.LifecycleException: Failed to start component [StandardService[Catalina]]
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:153)
     at org.apache.catalina.core.StandardServer.startInternal(StandardServer.java:756)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     ... 7 more
 Caused by: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina]]
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:153)
     at org.apache.catalina.core.StandardService.startInternal(StandardService.java:444)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     ... 9 more
 Caused by: org.apache.catalina.LifecycleException: A child container failed during start
     at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:1127)
     at org.apache.catalina.core.StandardEngine.startInternal(StandardEngine.java:300)
     at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
     ... 11 more

 ago 03, 2016 9:55:12 AM org.apache.coyote.AbstractProtocol pause
 INFORMAÇÕES: Pausing ProtocolHandler ["http-bio-8080"]
 ago 03, 2016 9:55:12 AM org.apache.coyote.AbstractProtocol pause
 INFORMAÇÕES: Pausing ProtocolHandler ["ajp-bio-8009"]
 ago 03, 2016 9:55:12 AM org.apache.catalina.core.StandardService stopInternal
 INFORMAÇÕES: Stopping service Catalina
 ago 03, 2016 9:55:12 AM org.apache.coyote.AbstractProtocol destroy
 INFORMAÇÕES: Destroying ProtocolHandler ["http-bio-8080"]
 ago 03, 2016 9:55:12 AM org.apache.coyote.AbstractProtocol destroy
 INFORMAÇÕES: Destroying ProtocolHandler ["ajp-bio-8009"]

aqui estar o web.xml

 <?xml version="1.0" encoding="UTF-8"?>
 <web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/javaee" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd" id="WebApp_ID" version="3.0">
   <display-name>HelloRest</display-name>
       <servlet-mapping>
           <servlet-name>javax.ws.rs.core.Application</servlet-name>
           <url-pattern>/rest/*</url-pattern>
       </servlet-mapping>
       <welcome-file-list></welcome-file-list>
 </web-app>

Você colocou os jars do JAX-RS no classpath da sua aplicação?

eu adicionei esses aqui

Retire o mapeamento servlet do web.xml, e crie a seguinte classe no seu projeto:

import javax.ws.rs.ApplicationPath;
import javax.ws.rs.core.Application;

@ApplicationPath("/rest")
public class ApplicationRest extends Application {

}

qual o propósito desta classe ?,

e para ajudar eu seguir as instruções desse tutorial aqui:
https://www.iit.bme.hu/~soi/Rest_HelloWorld_Tutorial.pdf