diff --git a/Schrick-Noah_Project-2.R b/Schrick-Noah_Project-2.R
index e792b04..0622f4f 100644
--- a/Schrick-Noah_Project-2.R
+++ b/Schrick-Noah_Project-2.R
@@ -26,7 +26,6 @@ findZeroBisect <- function(func, xl, xr, tol, maxsteps=1e6){
 fun.a <- function(x) {x^2-2}
 fun.a.string <- "x^2-2=0"
 sqrt2.estimate <- findZeroBisect(fun.a.string,1,2,1e-6)
-sqrt2.estimate[1]
 # Plot 1a
 if (!require("ggplot2")) install.packages("ggplot2")
 library(ggplot2)
@@ -43,9 +42,7 @@ ggplot(data.frame(x=seq(1,2,.1)), aes(x)) +
 fun.b <- function(x) {-3+x+2*exp(-x)}
 fun.b.string <- "-3+x+2*exp(-x)=0"
 fun.b.estimate.left <- findZeroBisect(fun.b,-2.5,0,1e-6)
-fun.b.estimate.left[1]
 fun.b.estimate.right <- findZeroBisect(fun.b,1,4,1e-6)
-fun.b.estimate.right[1]
 # Plot 1b
 ggplot(data.frame(x=seq(-2.5,5,.1)), aes(x)) + 
   stat_function(fun=fun.b, aes(col=fun.b.string)) + 
@@ -62,7 +59,6 @@ ggplot(data.frame(x=seq(-2.5,5,.1)), aes(x)) +
 fun.c <- function(x) {x^3-sin(x)^2}
 fun.c.string <- "x^3-sin(x)^2=0"
 fun.c.estimate <- findZeroBisect(fun.c,0.5,1,1e-6)
-fun.c.estimate[1]
 # Plot 1c
 ggplot(data.frame(x=seq(0.5,1,.1)), aes(x)) + 
   stat_function(fun=fun.c, aes(col=fun.c.string)) + 
@@ -73,4 +69,59 @@ ggplot(data.frame(x=seq(0.5,1,.1)), aes(x)) +
   xlab("x") + ylab("Zero Function") +
   theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
 
+## Part 2: Relaxation Method
+findZeroRelax <- function(g, x.guess, tol=1e-6, maxsteps=1e6){
+  steps <- 0
+  x.old <- x.guess
+  isConverged <- FALSE
+  while (!isConverged){
+    x.new <- g(x.old)
+    if(steps >= maxsteps || (abs(x.new-x.old)<tol)){
+      isConverged <- TRUE
+    }
+    else{
+      x.old <- x.new
+    }
+  steps <- steps + 1
+  }
+  return(c(x.new, g(x.new), steps))
+}
 
+# Solve 2b
+fun.2b <- function(x) {2-exp(-x)}
+fun.2b.fx <- function(x) {x-2+exp(-x)}
+fun.2b.string <- "x-2+exp(-x)"
+fun.2b.estimate <- findZeroRelax(fun.2b,0)
+# Find the other root with bisection
+fun.2b.bisect <- findZeroBisect(fun.2b,-2,0,1e-6)
+# Plot 2b
+ggplot(data.frame(x=seq(-2.5,2.5,.1)), aes(x)) + 
+  stat_function(fun=fun.2b.fx, aes(col=fun.2b.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.2b.estimate[1], 
+                 col = "relaxation estimate"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.2b.bisect[1],
+                 col = "bisection estimate"), show.legend=TRUE)+
+  ggtitle("Zero Function") +
+  xlab("x") + ylab("Zero Function") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
+
+# Solve 2c
+fun.2c <- function(x) {3-2*exp(-x)}
+fun.2c.fx <- function(x) {x+2*exp(-x)-3}
+fun.2c.string <- "x+2*exp(-x)-3"
+fun.2c.estimate <- findZeroRelax(fun.2c,-.5)
+fun.2c.estimate[1]
+# Find the other root with bisection
+fun.2c.bisect <- findZeroBisect(fun.2c,-1,0,1e-6)
+# Plot 2c
+ggplot(data.frame(x=seq(-1,4,.1)), aes(x)) + 
+  stat_function(fun=fun.2c.fx, aes(col=fun.2c.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.2c.estimate[1], 
+                 col = "relaxation estimate"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.2c.bisect[1], 
+                 col = "bisection estimate"), show.legend=TRUE)+
+  ggtitle("Zero Function") +
+  xlab("x") + ylab("Zero Function") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))