--- a/Fahad/Scala/Chapter5.sc	Sun Oct 26 11:17:40 2014 +0000
+++ b/Fahad/Scala/Chapter5.sc	Sun Oct 26 16:42:28 2014 +0000
@@ -28,28 +28,79 @@
   sumPowersOfTwo(2, 4)
   */
 
+  /*
   def sum(f: Int => Int, a: Int, b: Int): Int =
-    if (a > b) 0 else f(a) + sum(f, a + 1, b)     //> sum: (f: Int => Int, a: Int, b: Int)Int
+    if (a > b) 0 else f(a) + sum(f, a + 1, b)
 
   //def sumInts(a: Int, b: Int): Int = sum(id, a, b)
   //def sumInts(a: Int, b: Int): Int = sum((x: Int) => x, a, b)
   def sumInts(a: Int, b: Int): Int = sum(x => x, a, b)
-                                                  //> sumInts: (a: Int, b: Int)Int
   //def sumSquares(a: Int, b: Int): Int = sum(square, a, b)
   //def sumSquares(a: Int, b: Int): Int = sum((x: Int) => x * x, a, b)
   def sumSquares(a: Int, b: Int): Int = sum(x => x * x, a, b)
-                                                  //> sumSquares: (a: Int, b: Int)Int
   def sumPowersOfTwo(a: Int, b: Int): Int = sum(powerOfTwo, a, b)
-                                                  //> sumPowersOfTwo: (a: Int, b: Int)Int
   
-  def id(x: Int): Int = x                         //> id: (x: Int)Int
-	def square(x: Int): Int = x * x           //> square: (x: Int)Int
+  def id(x: Int): Int = x
+	def square(x: Int): Int = x * x
+	*/
 	def powerOfTwo(x: Int): Int = if (x == 0) 1 else 2 * powerOfTwo(x - 1)
                                                   //> powerOfTwo: (x: Int)Int
-                                                  
+  
+
   // 5.2: Currying
-  
-  
-  
+
+  def sum(f: Int => Int): (Int, Int) => Int = {
+    def sumF(a: Int, b: Int): Int =
+      if (a > b) 0 else f(a) + sumF(a + 1, b)
+    sumF
+  }                                               //> sum: (f: Int => Int)(Int, Int) => Int
+
+  def sumInts = sum(x => x)                       //> sumInts: => (Int, Int) => Int
+  def sumSquares = sum(x => x * x)                //> sumSquares: => (Int, Int) => Int
+  def sumPowersOfTwo = sum(powerOfTwo)            //> sumPowersOfTwo: => (Int, Int) => Int
   
+  sumSquares(1,10) + sumPowersOfTwo(10,20)        //> res0: Int = 2096513
+  sum(x => x * x)(2,4)                            //> res1: Int = 29
+
+	// 5.3: Finding Fixed Points of Functions
+	
+	val tolerance = 0.001                     //> tolerance  : Double = 0.001
+	def isCloseEnough(x: Double, y: Double) = Math.abs((x-y) / x) < tolerance
+                                                  //> isCloseEnough: (x: Double, y: Double)Boolean
+	def fixedPoint(f: Double => Double)(firstGuess: Double) = {
+		def iterate(guess: Double): Double = {
+			val next = f(guess)
+			if (isCloseEnough(guess, next)) next
+			else iterate(next)
+		}
+		iterate(firstGuess)
+	}                                         //> fixedPoint: (f: Double => Double)(firstGuess: Double)Double
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\ No newline at end of file