I can't speak for Eclipse's mistake, but in this specific case, you should be using the implicit JSP scriptlet variable application
and not be using HttpServlet
-inherited methods.
<script type="text/javascript" src="<%out.print(application.getContextPath());%>/js/jquery.js"></script>
<link rel="stylesheet" href="<%out.print(application.getContextPath());%>/css/home.css" />
Unrelated to the concrete problem, this is a 90's way of writing JSPs which is officially discouraged since JSP 2.0 which was released more than a decade ago. Are you sure you're reading up to date resources while learning JSP? You should be using EL expressions instead.
<script type="text/javascript" src="${pageContext.request.contextPath}/js/jquery.js"></script>
<link rel="stylesheet" href="${pageContext.request.contextPath}/css/home.css" />
Or, via <c:set>
to save the boilerplate:
<c:set var="root" value="${pageContext.request.contextPath}" />
...
<script type="text/javascript" src="${root}/js/jquery.js"></script>
<link rel="stylesheet" href="${root}/css/home.css" />