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+#Example 4     Chapter 9       Page no.: 282
+#Determining square root using Lagrange's interpolation
+
+#Given Table
+mydata<- data.frame(x=c(1,2,3,4,5),
+                    fx=c(sqrt(1), sqrt(2), sqrt(3), sqrt(4), sqrt(5)),
+                     stringsAsFactors = TRUE
+)
+mydata
+
+val<-mydata$x
+fun<-mydata$fx
+
+x0<-val[2]
+x1<-val[3]
+x2<-val[4]
+
+f0<-fun[2]
+f1<-fun[3]
+f2<-fun[4]
+
+var=2.5
+
+I0<- ((var-x1)*(var-x2))/((x0-x1)*(x0-x2))
+I0
+I1<- ((var-x0)*(var-x2))/((x1-x2)*(x1-x0))
+I1
+I2<-((var-x0)*(var-x1))/((x2-x0)*(x2-x1))
+I2
+
+Ans<- signif((f0*I0) + (f1*I1) + (f2*I2),5)
+cat("Calculated square root of 2.5 is :", Ans)
+
+Original<- signif(sqrt(var),5)
+cat("Original square root of 2.5 is :", Original)
+
+error<- Original-Ans
+cat("Error is :", error)