# File "Rsecant".  (related to Q1 of HW#2)

f = function(x) { x^2 * exp(-(x+sin(x))) }

g = fp = function(x) {2*x*exp(-(x+sin(x))) + x^2*exp(-(x+sin(x)))*(-1-cos(x))}

numits = 100

vallist = c(8,1)

for (i in 1:numits) {
    xprev = vallist[length(vallist)]
    xprevprev = vallist[length(vallist)-1]
    xnew = xprev - g(xprev) * (xprev-xprevprev) / (g(xprev) - g(xprevprev))
    vallist = c(vallist, xnew)
    if (xnew==xprev) {
	cat("answer equals:", xnew, "\n")
	break
    }
}

print(vallist)