diff --git a/analysisII.pdf b/analysisII.pdf
index f25ad81..1c1ffac 100644
Binary files a/analysisII.pdf and b/analysisII.pdf differ
diff --git a/analysisII.tex b/analysisII.tex
index 3d1f667..55100ea 100644
--- a/analysisII.tex
+++ b/analysisII.tex
@@ -20,5 +20,6 @@
 \input{ana2.tex}
 \input{ana3.tex}
 \input{ana4.tex}
+\input{ana5.tex}
 
 \end{document}