From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 50/CH2/EX2.16/2_16.PNG  | Bin 0 -> 11143 bytes
 50/CH2/EX2.16/ex_16.sce |  38 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 38 insertions(+)
 create mode 100755 50/CH2/EX2.16/2_16.PNG
 create mode 100755 50/CH2/EX2.16/ex_16.sce

(limited to '50/CH2/EX2.16')

diff --git a/50/CH2/EX2.16/2_16.PNG b/50/CH2/EX2.16/2_16.PNG
new file mode 100755
index 000000000..dd5cb960c
Binary files /dev/null and b/50/CH2/EX2.16/2_16.PNG differ
diff --git a/50/CH2/EX2.16/ex_16.sce b/50/CH2/EX2.16/ex_16.sce
new file mode 100755
index 000000000..d1a65a8ca
--- /dev/null
+++ b/50/CH2/EX2.16/ex_16.sce
@@ -0,0 +1,38 @@
+                                   // The equation x^3-5*x+1==0 has  real roots.
+                                   // the graph of this function can be observed here.
+xset('window',15);                                   
+x=-2:.01:4;                                             // defining the range of x.
+deff('[y]=f(x)','y=x^3-5*x+1');                  //defining the function.
+deff('[y]=fp(x)','y=3*x^2-5');
+deff('[y]=fpp(x)','y=6*x');
+y=feval(x,f);
+ 
+a=gca(); 
+ 
+a.y_location = "origin";
+ 
+a.x_location = "origin"; 
+plot(x,y)                                                  // instruction to plot the graph 
+title(' y = x^3-5*x+1')
+
+// from the above plot we can infre that the function has roots between   
+// the intervals (0,1),(2,3).
+// since we have been asked for the smallest positive root of the equation,
+// we are intrested on the interval (0,1)
+// a=0;b=1,
+
+
+//                solution by multipoint iteration method
+
+// the approximate  root after 3 iterations can be observed.
+
+
+multipoint_iteration31(0.5,f,fp)  
+
+// hence the approximate root  witin the permissible error of 10^-15 is .201640,
+
+
+
+multipoint_iteration33(0.5,f,fp)
+  
+// hence the approximate root  witin the permissible error of 10^-15 is .201640,
\ No newline at end of file
-- 
cgit